diff --git a/changelog.d/13755.misc b/changelog.d/13755.misc
new file mode 100644
index 000000000..662ee00e9
--- /dev/null
+++ b/changelog.d/13755.misc
@@ -0,0 +1 @@
+Re-type hint some collections as read-only.
diff --git a/synapse/app/phone_stats_home.py b/synapse/app/phone_stats_home.py
index 53db1e85b..897dd3eda 100644
--- a/synapse/app/phone_stats_home.py
+++ b/synapse/app/phone_stats_home.py
@@ -15,7 +15,7 @@ import logging
 import math
 import resource
 import sys
-from typing import TYPE_CHECKING, List, Sized, Tuple
+from typing import TYPE_CHECKING, List, Mapping, Sized, Tuple
 
 from prometheus_client import Gauge
 
@@ -194,7 +194,7 @@ def start_phone_stats_home(hs: "HomeServer") -> None:
     @wrap_as_background_process("generate_monthly_active_users")
     async def generate_monthly_active_users() -> None:
         current_mau_count = 0
-        current_mau_count_by_service = {}
+        current_mau_count_by_service: Mapping[str, int] = {}
         reserved_users: Sized = ()
         store = hs.get_datastores().main
         if hs.config.server.limit_usage_by_mau or hs.config.server.mau_stats_only:
diff --git a/synapse/config/room_directory.py b/synapse/config/room_directory.py
index 3ed236217..8666c22f0 100644
--- a/synapse/config/room_directory.py
+++ b/synapse/config/room_directory.py
@@ -13,7 +13,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-from typing import Any, List
+from typing import Any, Collection
 
 from matrix_common.regex import glob_to_regex
 
@@ -70,7 +70,7 @@ class RoomDirectoryConfig(Config):
         return False
 
     def is_publishing_room_allowed(
-        self, user_id: str, room_id: str, aliases: List[str]
+        self, user_id: str, room_id: str, aliases: Collection[str]
     ) -> bool:
         """Checks if the given user is allowed to publish the room
 
@@ -122,7 +122,7 @@ class _RoomDirectoryRule:
         except Exception as e:
             raise ConfigError("Failed to parse glob into regex") from e
 
-    def matches(self, user_id: str, room_id: str, aliases: List[str]) -> bool:
+    def matches(self, user_id: str, room_id: str, aliases: Collection[str]) -> bool:
         """Tests if this rule matches the given user_id, room_id and aliases.
 
         Args:
diff --git a/synapse/events/builder.py b/synapse/events/builder.py
index 94dd1298e..c82745275 100644
--- a/synapse/events/builder.py
+++ b/synapse/events/builder.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 import logging
-from typing import TYPE_CHECKING, Any, Dict, List, Optional, Tuple, Union
+from typing import TYPE_CHECKING, Any, Collection, Dict, List, Optional, Tuple, Union
 
 import attr
 from signedjson.types import SigningKey
@@ -103,7 +103,7 @@ class EventBuilder:
 
     async def build(
         self,
-        prev_event_ids: List[str],
+        prev_event_ids: Collection[str],
         auth_event_ids: Optional[List[str]],
         depth: Optional[int] = None,
     ) -> EventBase:
@@ -136,7 +136,7 @@ class EventBuilder:
 
         format_version = self.room_version.event_format
         # The types of auth/prev events changes between event versions.
-        prev_events: Union[List[str], List[Tuple[str, Dict[str, str]]]]
+        prev_events: Union[Collection[str], List[Tuple[str, Dict[str, str]]]]
         auth_events: Union[List[str], List[Tuple[str, Dict[str, str]]]]
         if format_version == EventFormatVersions.ROOM_V1_V2:
             auth_events = await self._store.add_event_hashes(auth_event_ids)
diff --git a/synapse/federation/federation_server.py b/synapse/federation/federation_server.py
index 8d3617248..6addc0bb6 100644
--- a/synapse/federation/federation_server.py
+++ b/synapse/federation/federation_server.py
@@ -23,6 +23,7 @@ from typing import (
     Collection,
     Dict,
     List,
+    Mapping,
     Optional,
     Tuple,
     Union,
@@ -1512,7 +1513,7 @@ class FederationHandlerRegistry:
 def _get_event_ids_for_partial_state_join(
     join_event: EventBase,
     prev_state_ids: StateMap[str],
-    summary: Dict[str, MemberSummary],
+    summary: Mapping[str, MemberSummary],
 ) -> Collection[str]:
     """Calculate state to be returned in a partial_state send_join
 
diff --git a/synapse/handlers/directory.py b/synapse/handlers/directory.py
index d31b0fbb1..a5798e948 100644
--- a/synapse/handlers/directory.py
+++ b/synapse/handlers/directory.py
@@ -14,7 +14,7 @@
 
 import logging
 import string
-from typing import TYPE_CHECKING, Iterable, List, Optional
+from typing import TYPE_CHECKING, Iterable, List, Optional, Sequence
 
 from typing_extensions import Literal
 
@@ -486,7 +486,7 @@ class DirectoryHandler:
             )
             if canonical_alias:
                 # Ensure we do not mutate room_aliases.
-                room_aliases = room_aliases + [canonical_alias]
+                room_aliases = list(room_aliases) + [canonical_alias]
 
             if not self.config.roomdirectory.is_publishing_room_allowed(
                 user_id, room_id, room_aliases
@@ -529,7 +529,7 @@ class DirectoryHandler:
 
     async def get_aliases_for_room(
         self, requester: Requester, room_id: str
-    ) -> List[str]:
+    ) -> Sequence[str]:
         """
         Get a list of the aliases that currently point to this room on this server
         """
diff --git a/synapse/handlers/receipts.py b/synapse/handlers/receipts.py
index 04c61ae3d..2bacdebfb 100644
--- a/synapse/handlers/receipts.py
+++ b/synapse/handlers/receipts.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 import logging
-from typing import TYPE_CHECKING, Iterable, List, Optional, Tuple
+from typing import TYPE_CHECKING, Iterable, List, Optional, Sequence, Tuple
 
 from synapse.api.constants import EduTypes, ReceiptTypes
 from synapse.appservice import ApplicationService
@@ -189,7 +189,7 @@ class ReceiptEventSource(EventSource[int, JsonDict]):
 
     @staticmethod
     def filter_out_private_receipts(
-        rooms: List[JsonDict], user_id: str
+        rooms: Sequence[JsonDict], user_id: str
     ) -> List[JsonDict]:
         """
         Filters a list of serialized receipts (as returned by /sync and /initialSync)
diff --git a/synapse/handlers/room.py b/synapse/handlers/room.py
index 0e759b8a5..060bbcb18 100644
--- a/synapse/handlers/room.py
+++ b/synapse/handlers/room.py
@@ -1928,6 +1928,6 @@ class RoomShutdownHandler:
         return {
             "kicked_users": kicked_users,
             "failed_to_kick_users": failed_to_kick_users,
-            "local_aliases": aliases_for_room,
+            "local_aliases": list(aliases_for_room),
             "new_room_id": new_room_id,
         }
diff --git a/synapse/handlers/sync.py b/synapse/handlers/sync.py
index 399685e5b..4bae46158 100644
--- a/synapse/handlers/sync.py
+++ b/synapse/handlers/sync.py
@@ -1519,7 +1519,7 @@ class SyncHandler:
             one_time_keys_count = await self.store.count_e2e_one_time_keys(
                 user_id, device_id
             )
-            unused_fallback_key_types = (
+            unused_fallback_key_types = list(
                 await self.store.get_e2e_unused_fallback_key_types(user_id, device_id)
             )
 
@@ -2301,7 +2301,7 @@ class SyncHandler:
         sync_result_builder: "SyncResultBuilder",
         room_builder: "RoomSyncResultBuilder",
         ephemeral: List[JsonDict],
-        tags: Optional[Dict[str, Dict[str, Any]]],
+        tags: Optional[Mapping[str, Mapping[str, Any]]],
         account_data: Mapping[str, JsonDict],
         always_include: bool = False,
     ) -> None:
diff --git a/synapse/push/bulk_push_rule_evaluator.py b/synapse/push/bulk_push_rule_evaluator.py
index 8568aca52..f6a5bffb0 100644
--- a/synapse/push/bulk_push_rule_evaluator.py
+++ b/synapse/push/bulk_push_rule_evaluator.py
@@ -22,6 +22,7 @@ from typing import (
     List,
     Mapping,
     Optional,
+    Sequence,
     Set,
     Tuple,
     Union,
@@ -149,7 +150,7 @@ class BulkPushRuleEvaluator:
         # little, we can skip fetching a huge number of push rules in large rooms.
         # This helps make joins and leaves faster.
         if event.type == EventTypes.Member:
-            local_users = []
+            local_users: Sequence[str] = []
             # We never notify a user about their own actions. This is enforced in
             # `_action_for_event_by_user` in the loop over `rules_by_user`, but we
             # do the same check here to avoid unnecessary DB queries.
@@ -184,7 +185,6 @@ class BulkPushRuleEvaluator:
         if event.type == EventTypes.Member and event.membership == Membership.INVITE:
             invited = event.state_key
             if invited and self.hs.is_mine_id(invited) and invited not in local_users:
-                local_users = list(local_users)
                 local_users.append(invited)
 
         if not local_users:
diff --git a/synapse/state/__init__.py b/synapse/state/__init__.py
index e877e6f1a..4dc25df67 100644
--- a/synapse/state/__init__.py
+++ b/synapse/state/__init__.py
@@ -226,7 +226,7 @@ class StateHandler:
         return await ret.get_state(self._state_storage_controller, state_filter)
 
     async def get_current_user_ids_in_room(
-        self, room_id: str, latest_event_ids: List[str]
+        self, room_id: str, latest_event_ids: Collection[str]
     ) -> Set[str]:
         """
         Get the users IDs who are currently in a room.
diff --git a/synapse/storage/controllers/state.py b/synapse/storage/controllers/state.py
index 52efd4a17..9d7a8a792 100644
--- a/synapse/storage/controllers/state.py
+++ b/synapse/storage/controllers/state.py
@@ -14,6 +14,7 @@
 import logging
 from typing import (
     TYPE_CHECKING,
+    AbstractSet,
     Any,
     Awaitable,
     Callable,
@@ -23,7 +24,6 @@ from typing import (
     List,
     Mapping,
     Optional,
-    Set,
     Tuple,
 )
 
@@ -527,7 +527,7 @@ class StateStorageController:
         )
         return state_map.get(key)
 
-    async def get_current_hosts_in_room(self, room_id: str) -> Set[str]:
+    async def get_current_hosts_in_room(self, room_id: str) -> AbstractSet[str]:
         """Get current hosts in room based on current state.
 
         Blocks until we have full state for the given room. This only happens for rooms
@@ -584,7 +584,7 @@ class StateStorageController:
 
     async def get_users_in_room_with_profiles(
         self, room_id: str
-    ) -> Dict[str, ProfileInfo]:
+    ) -> Mapping[str, ProfileInfo]:
         """
         Get the current users in the room with their profiles.
         If the room is currently partial-stated, this will block until the room has
diff --git a/synapse/storage/databases/main/account_data.py b/synapse/storage/databases/main/account_data.py
index 2d6f02c14..95567826f 100644
--- a/synapse/storage/databases/main/account_data.py
+++ b/synapse/storage/databases/main/account_data.py
@@ -240,7 +240,7 @@ class AccountDataWorkerStore(PushRulesWorkerStore, CacheInvalidationWorkerStore)
     @cached(num_args=2, tree=True)
     async def get_account_data_for_room(
         self, user_id: str, room_id: str
-    ) -> Dict[str, JsonDict]:
+    ) -> Mapping[str, JsonDict]:
         """Get all the client account_data for a user for a room.
 
         Args:
diff --git a/synapse/storage/databases/main/appservice.py b/synapse/storage/databases/main/appservice.py
index 5fb152c4f..484db175d 100644
--- a/synapse/storage/databases/main/appservice.py
+++ b/synapse/storage/databases/main/appservice.py
@@ -166,7 +166,7 @@ class ApplicationServiceWorkerStore(RoomMemberWorkerStore):
         room_id: str,
         app_service: "ApplicationService",
         cache_context: _CacheContext,
-    ) -> List[str]:
+    ) -> Sequence[str]:
         """
         Get all users in a room that the appservice controls.
 
diff --git a/synapse/storage/databases/main/devices.py b/synapse/storage/databases/main/devices.py
index 85c1778a8..1ca66d57d 100644
--- a/synapse/storage/databases/main/devices.py
+++ b/synapse/storage/databases/main/devices.py
@@ -21,6 +21,7 @@ from typing import (
     Dict,
     Iterable,
     List,
+    Mapping,
     Optional,
     Set,
     Tuple,
@@ -202,7 +203,9 @@ class DeviceWorkerStore(RoomMemberWorkerStore, EndToEndKeyWorkerStore):
     def get_device_stream_token(self) -> int:
         return self._device_list_id_gen.get_current_token()
 
-    async def count_devices_by_users(self, user_ids: Optional[List[str]] = None) -> int:
+    async def count_devices_by_users(
+        self, user_ids: Optional[Collection[str]] = None
+    ) -> int:
         """Retrieve number of all devices of given users.
         Only returns number of devices that are not marked as hidden.
 
@@ -213,7 +216,7 @@ class DeviceWorkerStore(RoomMemberWorkerStore, EndToEndKeyWorkerStore):
         """
 
         def count_devices_by_users_txn(
-            txn: LoggingTransaction, user_ids: List[str]
+            txn: LoggingTransaction, user_ids: Collection[str]
         ) -> int:
             sql = """
                 SELECT count(*)
@@ -747,7 +750,7 @@ class DeviceWorkerStore(RoomMemberWorkerStore, EndToEndKeyWorkerStore):
     @cancellable
     async def get_user_devices_from_cache(
         self, user_ids: Set[str], user_and_device_ids: List[Tuple[str, str]]
-    ) -> Tuple[Set[str], Dict[str, Dict[str, JsonDict]]]:
+    ) -> Tuple[Set[str], Dict[str, Mapping[str, JsonDict]]]:
         """Get the devices (and keys if any) for remote users from the cache.
 
         Args:
@@ -775,16 +778,18 @@ class DeviceWorkerStore(RoomMemberWorkerStore, EndToEndKeyWorkerStore):
         user_ids_not_in_cache = unique_user_ids - user_ids_in_cache
 
         # First fetch all the users which all devices are to be returned.
-        results: Dict[str, Dict[str, JsonDict]] = {}
+        results: Dict[str, Mapping[str, JsonDict]] = {}
         for user_id in user_ids:
             if user_id in user_ids_in_cache:
                 results[user_id] = await self.get_cached_devices_for_user(user_id)
         # Then fetch all device-specific requests, but skip users we've already
         # fetched all devices for.
+        device_specific_results: Dict[str, Dict[str, JsonDict]] = {}
         for user_id, device_id in user_and_device_ids:
             if user_id in user_ids_in_cache and user_id not in user_ids:
                 device = await self._get_cached_user_device(user_id, device_id)
-                results.setdefault(user_id, {})[device_id] = device
+                device_specific_results.setdefault(user_id, {})[device_id] = device
+        results.update(device_specific_results)
 
         set_tag("in_cache", str(results))
         set_tag("not_in_cache", str(user_ids_not_in_cache))
@@ -802,7 +807,7 @@ class DeviceWorkerStore(RoomMemberWorkerStore, EndToEndKeyWorkerStore):
         return db_to_json(content)
 
     @cached()
-    async def get_cached_devices_for_user(self, user_id: str) -> Dict[str, JsonDict]:
+    async def get_cached_devices_for_user(self, user_id: str) -> Mapping[str, JsonDict]:
         devices = await self.db_pool.simple_select_list(
             table="device_lists_remote_cache",
             keyvalues={"user_id": user_id},
diff --git a/synapse/storage/databases/main/directory.py b/synapse/storage/databases/main/directory.py
index 5903fdaf0..44aa18117 100644
--- a/synapse/storage/databases/main/directory.py
+++ b/synapse/storage/databases/main/directory.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-from typing import Iterable, List, Optional, Tuple
+from typing import Iterable, List, Optional, Sequence, Tuple
 
 import attr
 
@@ -74,7 +74,7 @@ class DirectoryWorkerStore(CacheInvalidationWorkerStore):
         )
 
     @cached(max_entries=5000)
-    async def get_aliases_for_room(self, room_id: str) -> List[str]:
+    async def get_aliases_for_room(self, room_id: str) -> Sequence[str]:
         return await self.db_pool.simple_select_onecol(
             "room_aliases",
             {"room_id": room_id},
diff --git a/synapse/storage/databases/main/end_to_end_keys.py b/synapse/storage/databases/main/end_to_end_keys.py
index c4ac6c33b..752dc16e1 100644
--- a/synapse/storage/databases/main/end_to_end_keys.py
+++ b/synapse/storage/databases/main/end_to_end_keys.py
@@ -20,7 +20,9 @@ from typing import (
     Dict,
     Iterable,
     List,
+    Mapping,
     Optional,
+    Sequence,
     Tuple,
     Union,
     cast,
@@ -691,7 +693,7 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore, CacheInvalidationWorker
     @cached(max_entries=10000)
     async def get_e2e_unused_fallback_key_types(
         self, user_id: str, device_id: str
-    ) -> List[str]:
+    ) -> Sequence[str]:
         """Returns the fallback key types that have an unused key.
 
         Args:
@@ -731,7 +733,7 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore, CacheInvalidationWorker
         return user_keys.get(key_type)
 
     @cached(num_args=1)
-    def _get_bare_e2e_cross_signing_keys(self, user_id: str) -> Dict[str, JsonDict]:
+    def _get_bare_e2e_cross_signing_keys(self, user_id: str) -> Mapping[str, JsonDict]:
         """Dummy function.  Only used to make a cache for
         _get_bare_e2e_cross_signing_keys_bulk.
         """
@@ -744,7 +746,7 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore, CacheInvalidationWorker
     )
     async def _get_bare_e2e_cross_signing_keys_bulk(
         self, user_ids: Iterable[str]
-    ) -> Dict[str, Optional[Dict[str, JsonDict]]]:
+    ) -> Dict[str, Optional[Mapping[str, JsonDict]]]:
         """Returns the cross-signing keys for a set of users.  The output of this
         function should be passed to _get_e2e_cross_signing_signatures_txn if
         the signatures for the calling user need to be fetched.
@@ -765,7 +767,7 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore, CacheInvalidationWorker
         )
 
         # The `Optional` comes from the `@cachedList` decorator.
-        return cast(Dict[str, Optional[Dict[str, JsonDict]]], result)
+        return cast(Dict[str, Optional[Mapping[str, JsonDict]]], result)
 
     def _get_bare_e2e_cross_signing_keys_bulk_txn(
         self,
@@ -924,7 +926,7 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore, CacheInvalidationWorker
     @cancellable
     async def get_e2e_cross_signing_keys_bulk(
         self, user_ids: List[str], from_user_id: Optional[str] = None
-    ) -> Dict[str, Optional[Dict[str, JsonDict]]]:
+    ) -> Dict[str, Optional[Mapping[str, JsonDict]]]:
         """Returns the cross-signing keys for a set of users.
 
         Args:
@@ -940,11 +942,14 @@ class EndToEndKeyWorkerStore(EndToEndKeyBackgroundStore, CacheInvalidationWorker
         result = await self._get_bare_e2e_cross_signing_keys_bulk(user_ids)
 
         if from_user_id:
-            result = await self.db_pool.runInteraction(
-                "get_e2e_cross_signing_signatures",
-                self._get_e2e_cross_signing_signatures_txn,
-                result,
-                from_user_id,
+            result = cast(
+                Dict[str, Optional[Mapping[str, JsonDict]]],
+                await self.db_pool.runInteraction(
+                    "get_e2e_cross_signing_signatures",
+                    self._get_e2e_cross_signing_signatures_txn,
+                    result,
+                    from_user_id,
+                ),
             )
 
         return result
diff --git a/synapse/storage/databases/main/event_federation.py b/synapse/storage/databases/main/event_federation.py
index bbee02ab1..ca780cca3 100644
--- a/synapse/storage/databases/main/event_federation.py
+++ b/synapse/storage/databases/main/event_federation.py
@@ -22,6 +22,7 @@ from typing import (
     Iterable,
     List,
     Optional,
+    Sequence,
     Set,
     Tuple,
     cast,
@@ -1004,7 +1005,9 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
             room_id,
         )
 
-    async def get_max_depth_of(self, event_ids: List[str]) -> Tuple[Optional[str], int]:
+    async def get_max_depth_of(
+        self, event_ids: Collection[str]
+    ) -> Tuple[Optional[str], int]:
         """Returns the event ID and depth for the event that has the max depth from a set of event IDs
 
         Args:
@@ -1141,7 +1144,7 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
         )
 
     @cached(max_entries=5000, iterable=True)
-    async def get_latest_event_ids_in_room(self, room_id: str) -> List[str]:
+    async def get_latest_event_ids_in_room(self, room_id: str) -> Sequence[str]:
         return await self.db_pool.simple_select_onecol(
             table="event_forward_extremities",
             keyvalues={"room_id": room_id},
@@ -1171,7 +1174,7 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
     @cancellable
     async def get_forward_extremities_for_room_at_stream_ordering(
         self, room_id: str, stream_ordering: int
-    ) -> List[str]:
+    ) -> Sequence[str]:
         """For a given room_id and stream_ordering, return the forward
         extremeties of the room at that point in "time".
 
@@ -1204,7 +1207,7 @@ class EventFederationWorkerStore(SignatureWorkerStore, EventsWorkerStore, SQLBas
     @cached(max_entries=5000, num_args=2)
     async def _get_forward_extremeties_for_room(
         self, room_id: str, stream_ordering: int
-    ) -> List[str]:
+    ) -> Sequence[str]:
         """For a given room_id and stream_ordering, return the forward
         extremeties of the room at that point in "time".
 
diff --git a/synapse/storage/databases/main/monthly_active_users.py b/synapse/storage/databases/main/monthly_active_users.py
index db9a24db5..4b1061e6d 100644
--- a/synapse/storage/databases/main/monthly_active_users.py
+++ b/synapse/storage/databases/main/monthly_active_users.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 import logging
-from typing import TYPE_CHECKING, Dict, List, Optional, Tuple, cast
+from typing import TYPE_CHECKING, Dict, List, Mapping, Optional, Tuple, cast
 
 from synapse.metrics.background_process_metrics import wrap_as_background_process
 from synapse.storage.database import (
@@ -95,7 +95,7 @@ class MonthlyActiveUsersWorkerStore(RegistrationWorkerStore):
         return await self.db_pool.runInteraction("count_users", _count_users)
 
     @cached(num_args=0)
-    async def get_monthly_active_count_by_service(self) -> Dict[str, int]:
+    async def get_monthly_active_count_by_service(self) -> Mapping[str, int]:
         """Generates current count of monthly active users broken down by service.
         A service is typically an appservice but also includes native matrix users.
         Since the `monthly_active_users` table is populated from the `user_ips` table
diff --git a/synapse/storage/databases/main/receipts.py b/synapse/storage/databases/main/receipts.py
index 29972d520..dddf49c2d 100644
--- a/synapse/storage/databases/main/receipts.py
+++ b/synapse/storage/databases/main/receipts.py
@@ -21,7 +21,9 @@ from typing import (
     Dict,
     Iterable,
     List,
+    Mapping,
     Optional,
+    Sequence,
     Tuple,
     cast,
 )
@@ -288,7 +290,7 @@ class ReceiptsWorkerStore(SQLBaseStore):
 
     async def get_linearized_receipts_for_room(
         self, room_id: str, to_key: int, from_key: Optional[int] = None
-    ) -> List[dict]:
+    ) -> Sequence[JsonDict]:
         """Get receipts for a single room for sending to clients.
 
         Args:
@@ -311,7 +313,7 @@ class ReceiptsWorkerStore(SQLBaseStore):
     @cached(tree=True)
     async def _get_linearized_receipts_for_room(
         self, room_id: str, to_key: int, from_key: Optional[int] = None
-    ) -> List[JsonDict]:
+    ) -> Sequence[JsonDict]:
         """See get_linearized_receipts_for_room"""
 
         def f(txn: LoggingTransaction) -> List[Dict[str, Any]]:
@@ -354,7 +356,7 @@ class ReceiptsWorkerStore(SQLBaseStore):
     )
     async def _get_linearized_receipts_for_rooms(
         self, room_ids: Collection[str], to_key: int, from_key: Optional[int] = None
-    ) -> Dict[str, List[JsonDict]]:
+    ) -> Dict[str, Sequence[JsonDict]]:
         if not room_ids:
             return {}
 
@@ -416,7 +418,7 @@ class ReceiptsWorkerStore(SQLBaseStore):
     )
     async def get_linearized_receipts_for_all_rooms(
         self, to_key: int, from_key: Optional[int] = None
-    ) -> Dict[str, JsonDict]:
+    ) -> Mapping[str, JsonDict]:
         """Get receipts for all rooms between two stream_ids, up
         to a limit of the latest 100 read receipts.
 
diff --git a/synapse/storage/databases/main/registration.py b/synapse/storage/databases/main/registration.py
index 31f0f2bd3..9a55e1762 100644
--- a/synapse/storage/databases/main/registration.py
+++ b/synapse/storage/databases/main/registration.py
@@ -16,7 +16,7 @@
 import logging
 import random
 import re
-from typing import TYPE_CHECKING, Any, Dict, List, Optional, Tuple, Union, cast
+from typing import TYPE_CHECKING, Any, Dict, List, Mapping, Optional, Tuple, Union, cast
 
 import attr
 
@@ -192,7 +192,7 @@ class RegistrationWorkerStore(CacheInvalidationWorkerStore):
             )
 
     @cached()
-    async def get_user_by_id(self, user_id: str) -> Optional[Dict[str, Any]]:
+    async def get_user_by_id(self, user_id: str) -> Optional[Mapping[str, Any]]:
         """Deprecated: use get_userinfo_by_id instead"""
 
         def get_user_by_id_txn(txn: LoggingTransaction) -> Optional[Dict[str, Any]]:
diff --git a/synapse/storage/databases/main/relations.py b/synapse/storage/databases/main/relations.py
index 0018d6f7a..fa3266c08 100644
--- a/synapse/storage/databases/main/relations.py
+++ b/synapse/storage/databases/main/relations.py
@@ -22,6 +22,7 @@ from typing import (
     List,
     Mapping,
     Optional,
+    Sequence,
     Set,
     Tuple,
     Union,
@@ -171,7 +172,7 @@ class RelationsWorkerStore(SQLBaseStore):
         direction: Direction = Direction.BACKWARDS,
         from_token: Optional[StreamToken] = None,
         to_token: Optional[StreamToken] = None,
-    ) -> Tuple[List[_RelatedEvent], Optional[StreamToken]]:
+    ) -> Tuple[Sequence[_RelatedEvent], Optional[StreamToken]]:
         """Get a list of relations for an event, ordered by topological ordering.
 
         Args:
@@ -397,7 +398,9 @@ class RelationsWorkerStore(SQLBaseStore):
         return result is not None
 
     @cached()
-    async def get_aggregation_groups_for_event(self, event_id: str) -> List[JsonDict]:
+    async def get_aggregation_groups_for_event(
+        self, event_id: str
+    ) -> Sequence[JsonDict]:
         raise NotImplementedError()
 
     @cachedList(
diff --git a/synapse/storage/databases/main/roommember.py b/synapse/storage/databases/main/roommember.py
index ea6a5e2f3..694a5b802 100644
--- a/synapse/storage/databases/main/roommember.py
+++ b/synapse/storage/databases/main/roommember.py
@@ -24,6 +24,7 @@ from typing import (
     List,
     Mapping,
     Optional,
+    Sequence,
     Set,
     Tuple,
     Union,
@@ -153,7 +154,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         return self._known_servers_count
 
     @cached(max_entries=100000, iterable=True)
-    async def get_users_in_room(self, room_id: str) -> List[str]:
+    async def get_users_in_room(self, room_id: str) -> Sequence[str]:
         """Returns a list of users in the room.
 
         Will return inaccurate results for rooms with partial state, since the state for
@@ -190,9 +191,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         )
 
     @cached()
-    def get_user_in_room_with_profile(
-        self, room_id: str, user_id: str
-    ) -> Dict[str, ProfileInfo]:
+    def get_user_in_room_with_profile(self, room_id: str, user_id: str) -> ProfileInfo:
         raise NotImplementedError()
 
     @cachedList(
@@ -246,7 +245,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
     @cached(max_entries=100000, iterable=True)
     async def get_users_in_room_with_profiles(
         self, room_id: str
-    ) -> Dict[str, ProfileInfo]:
+    ) -> Mapping[str, ProfileInfo]:
         """Get a mapping from user ID to profile information for all users in a given room.
 
         The profile information comes directly from this room's `m.room.member`
@@ -285,7 +284,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         )
 
     @cached(max_entries=100000)
-    async def get_room_summary(self, room_id: str) -> Dict[str, MemberSummary]:
+    async def get_room_summary(self, room_id: str) -> Mapping[str, MemberSummary]:
         """Get the details of a room roughly suitable for use by the room
         summary extension to /sync. Useful when lazy loading room members.
         Args:
@@ -357,7 +356,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
     @cached()
     async def get_invited_rooms_for_local_user(
         self, user_id: str
-    ) -> List[RoomsForUser]:
+    ) -> Sequence[RoomsForUser]:
         """Get all the rooms the *local* user is invited to.
 
         Args:
@@ -475,7 +474,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         return results
 
     @cached(iterable=True)
-    async def get_local_users_in_room(self, room_id: str) -> List[str]:
+    async def get_local_users_in_room(self, room_id: str) -> Sequence[str]:
         """
         Retrieves a list of the current roommembers who are local to the server.
         """
@@ -791,7 +790,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         """Returns the set of users who share a room with `user_id`"""
         room_ids = await self.get_rooms_for_user(user_id)
 
-        user_who_share_room = set()
+        user_who_share_room: Set[str] = set()
         for room_id in room_ids:
             user_ids = await self.get_users_in_room(room_id)
             user_who_share_room.update(user_ids)
@@ -953,7 +952,7 @@ class RoomMemberWorkerStore(EventsWorkerStore):
         return True
 
     @cached(iterable=True, max_entries=10000)
-    async def get_current_hosts_in_room(self, room_id: str) -> Set[str]:
+    async def get_current_hosts_in_room(self, room_id: str) -> AbstractSet[str]:
         """Get current hosts in room based on current state."""
 
         # First we check if we already have `get_users_in_room` in the cache, as
diff --git a/synapse/storage/databases/main/signatures.py b/synapse/storage/databases/main/signatures.py
index 05da15074..5dcb1fc0b 100644
--- a/synapse/storage/databases/main/signatures.py
+++ b/synapse/storage/databases/main/signatures.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-from typing import Collection, Dict, List, Tuple
+from typing import Collection, Dict, List, Mapping, Tuple
 
 from unpaddedbase64 import encode_base64
 
@@ -26,7 +26,7 @@ from synapse.util.caches.descriptors import cached, cachedList
 
 class SignatureWorkerStore(EventsWorkerStore):
     @cached()
-    def get_event_reference_hash(self, event_id: str) -> Dict[str, Dict[str, bytes]]:
+    def get_event_reference_hash(self, event_id: str) -> Mapping[str, bytes]:
         # This is a dummy function to allow get_event_reference_hashes
         # to use its cache
         raise NotImplementedError()
@@ -36,7 +36,7 @@ class SignatureWorkerStore(EventsWorkerStore):
     )
     async def get_event_reference_hashes(
         self, event_ids: Collection[str]
-    ) -> Dict[str, Dict[str, bytes]]:
+    ) -> Mapping[str, Mapping[str, bytes]]:
         """Get all hashes for given events.
 
         Args:
diff --git a/synapse/storage/databases/main/tags.py b/synapse/storage/databases/main/tags.py
index d5500cdd4..c149a9eac 100644
--- a/synapse/storage/databases/main/tags.py
+++ b/synapse/storage/databases/main/tags.py
@@ -15,7 +15,7 @@
 # limitations under the License.
 
 import logging
-from typing import Any, Dict, Iterable, List, Tuple, cast
+from typing import Any, Dict, Iterable, List, Mapping, Tuple, cast
 
 from synapse.api.constants import AccountDataTypes
 from synapse.replication.tcp.streams import AccountDataStream
@@ -32,7 +32,9 @@ logger = logging.getLogger(__name__)
 
 class TagsWorkerStore(AccountDataWorkerStore):
     @cached()
-    async def get_tags_for_user(self, user_id: str) -> Dict[str, Dict[str, JsonDict]]:
+    async def get_tags_for_user(
+        self, user_id: str
+    ) -> Mapping[str, Mapping[str, JsonDict]]:
         """Get all the tags for a user.
 
 
@@ -107,7 +109,7 @@ class TagsWorkerStore(AccountDataWorkerStore):
 
     async def get_updated_tags(
         self, user_id: str, stream_id: int
-    ) -> Dict[str, Dict[str, JsonDict]]:
+    ) -> Mapping[str, Mapping[str, JsonDict]]:
         """Get all the tags for the rooms where the tags have changed since the
         given version
 
diff --git a/synapse/storage/databases/main/user_directory.py b/synapse/storage/databases/main/user_directory.py
index 14ef5b040..f6a6fd407 100644
--- a/synapse/storage/databases/main/user_directory.py
+++ b/synapse/storage/databases/main/user_directory.py
@@ -16,9 +16,9 @@ import logging
 import re
 from typing import (
     TYPE_CHECKING,
-    Dict,
     Iterable,
     List,
+    Mapping,
     Optional,
     Sequence,
     Set,
@@ -586,7 +586,7 @@ class UserDirectoryBackgroundUpdateStore(StateDeltasStore):
         )
 
     @cached()
-    async def get_user_in_directory(self, user_id: str) -> Optional[Dict[str, str]]:
+    async def get_user_in_directory(self, user_id: str) -> Optional[Mapping[str, str]]:
         return await self.db_pool.simple_select_one(
             table="user_directory",
             keyvalues={"user_id": user_id},
diff --git a/tests/rest/admin/test_server_notice.py b/tests/rest/admin/test_server_notice.py
index a2f347f66..f71ff46d8 100644
--- a/tests/rest/admin/test_server_notice.py
+++ b/tests/rest/admin/test_server_notice.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import List
+from typing import List, Sequence
 
 from twisted.test.proto_helpers import MemoryReactor
 
@@ -558,7 +558,7 @@ class ServerNoticeTestCase(unittest.HomeserverTestCase):
 
     def _check_invite_and_join_status(
         self, user_id: str, expected_invites: int, expected_memberships: int
-    ) -> List[RoomsForUser]:
+    ) -> Sequence[RoomsForUser]:
         """Check invite and room membership status of a user.
 
         Args