diff --git a/.buildkite/docker-compose.py27.pg94.yaml b/.buildkite/docker-compose.py27.pg94.yaml
deleted file mode 100644
index 2d4b9eadd..000000000
--- a/.buildkite/docker-compose.py27.pg94.yaml
+++ /dev/null
@@ -1,21 +0,0 @@
-version: '3.1'
-
-services:
-
-  postgres:
-    image: postgres:9.4
-    environment:
-      POSTGRES_PASSWORD: postgres
-
-  testenv:
-    image: python:2.7
-    depends_on:
-      - postgres
-    env_file: .env
-    environment:
-      SYNAPSE_POSTGRES_HOST: postgres
-      SYNAPSE_POSTGRES_USER: postgres
-      SYNAPSE_POSTGRES_PASSWORD: postgres
-    working_dir: /app
-    volumes:
-      - ..:/app
diff --git a/.buildkite/docker-compose.py27.pg95.yaml b/.buildkite/docker-compose.py27.pg95.yaml
deleted file mode 100644
index c6a41f1da..000000000
--- a/.buildkite/docker-compose.py27.pg95.yaml
+++ /dev/null
@@ -1,21 +0,0 @@
-version: '3.1'
-
-services:
-
-  postgres:
-    image: postgres:9.5
-    environment:
-      POSTGRES_PASSWORD: postgres
-
-  testenv:
-    image: python:2.7
-    depends_on:
-      - postgres
-    env_file: .env
-    environment:
-      SYNAPSE_POSTGRES_HOST: postgres
-      SYNAPSE_POSTGRES_USER: postgres
-      SYNAPSE_POSTGRES_PASSWORD: postgres
-    working_dir: /app
-    volumes:
-      - ..:/app
diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index 719f22b4e..8eddf8b93 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -48,13 +48,13 @@ steps:
 
   - command:
       - "python -m pip install tox"
-      - "tox -e py27,codecov"
-    label: ":python: 2.7 / SQLite"
+      - "tox -e py35-old,codecov"
+    label: ":python: 3.5 / SQLite / Old Deps"
     env:
       TRIAL_FLAGS: "-j 2"
     plugins:
       - docker#v3.0.1:
-          image: "python:2.7"
+          image: "python:3.5"
           propagate-environment: true
     retry:
       automatic:
@@ -114,57 +114,6 @@ steps:
         - exit_status: 2
           limit: 2
 
-  - command:
-      - "python -m pip install tox"
-      - "tox -e py27-old,codecov"
-    label: ":python: 2.7 / SQLite / Old Deps"
-    env:
-      TRIAL_FLAGS: "-j 2"
-    plugins:
-      - docker#v3.0.1:
-          image: "python:2.7"
-          propagate-environment: true
-    retry:
-      automatic:
-        - exit_status: -1
-          limit: 2
-        - exit_status: 2
-          limit: 2
-
-  - label: ":python: 2.7 / :postgres: 9.4"
-    env:
-      TRIAL_FLAGS: "-j 4"
-    command:
-      - "bash -c 'python -m pip install tox && python -m tox -e py27-postgres,codecov'"
-    plugins:
-      - docker-compose#v2.1.0:
-          run: testenv
-          config:
-            - .buildkite/docker-compose.py27.pg94.yaml
-    retry:
-      automatic:
-        - exit_status: -1
-          limit: 2
-        - exit_status: 2
-          limit: 2
-
-  - label: ":python: 2.7 / :postgres: 9.5"
-    env:
-      TRIAL_FLAGS: "-j 4"
-    command:
-      - "bash -c 'python -m pip install tox && python -m tox -e py27-postgres,codecov'"
-    plugins:
-      - docker-compose#v2.1.0:
-          run: testenv
-          config:
-            - .buildkite/docker-compose.py27.pg95.yaml
-    retry:
-      automatic:
-        - exit_status: -1
-          limit: 2
-        - exit_status: 2
-          limit: 2
-
   - label: ":python: 3.5 / :postgres: 9.4"
     env:
       TRIAL_FLAGS: "-j 4"
diff --git a/.circleci/config.yml b/.circleci/config.yml
index 137747dae..3c2b32c01 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -4,72 +4,18 @@ jobs:
     machine: true
     steps:
       - checkout
-      - run: docker build -f docker/Dockerfile --label gitsha1=${CIRCLE_SHA1} -t matrixdotorg/synapse:${CIRCLE_TAG}-py2 .
       - run: docker build -f docker/Dockerfile --label gitsha1=${CIRCLE_SHA1} -t matrixdotorg/synapse:${CIRCLE_TAG} -t matrixdotorg/synapse:${CIRCLE_TAG}-py3 --build-arg PYTHON_VERSION=3.6 .
       - run: docker login --username $DOCKER_HUB_USERNAME --password $DOCKER_HUB_PASSWORD
       - run: docker push matrixdotorg/synapse:${CIRCLE_TAG}
-      - run: docker push matrixdotorg/synapse:${CIRCLE_TAG}-py2
       - run: docker push matrixdotorg/synapse:${CIRCLE_TAG}-py3
   dockerhubuploadlatest:
     machine: true
     steps:
       - checkout
-      - run: docker build -f docker/Dockerfile --label gitsha1=${CIRCLE_SHA1} -t matrixdotorg/synapse:latest-py2 .
       - run: docker build -f docker/Dockerfile --label gitsha1=${CIRCLE_SHA1} -t matrixdotorg/synapse:latest -t matrixdotorg/synapse:latest-py3 --build-arg PYTHON_VERSION=3.6 .
       - run: docker login --username $DOCKER_HUB_USERNAME --password $DOCKER_HUB_PASSWORD
       - run: docker push matrixdotorg/synapse:latest
-      - run: docker push matrixdotorg/synapse:latest-py2
       - run: docker push matrixdotorg/synapse:latest-py3
-  sytestpy2:
-    docker:
-      - image: matrixdotorg/sytest-synapsepy2
-    working_directory: /src
-    steps:
-      - checkout
-      - run: /synapse_sytest.sh
-      - store_artifacts:
-          path: /logs
-          destination: logs
-      - store_test_results:
-          path: /logs
-  sytestpy2postgres:
-    docker:
-      - image: matrixdotorg/sytest-synapsepy2
-    working_directory: /src
-    steps:
-      - checkout
-      - run: POSTGRES=1 /synapse_sytest.sh
-      - store_artifacts:
-          path: /logs
-          destination: logs
-      - store_test_results:
-          path: /logs
-  sytestpy2merged:
-    docker:
-      - image: matrixdotorg/sytest-synapsepy2
-    working_directory: /src
-    steps:
-      - checkout
-      - run: bash .circleci/merge_base_branch.sh
-      - run: /synapse_sytest.sh
-      - store_artifacts:
-          path: /logs
-          destination: logs
-      - store_test_results:
-          path: /logs
-  sytestpy2postgresmerged:
-    docker:
-      - image: matrixdotorg/sytest-synapsepy2
-    working_directory: /src
-    steps:
-      - checkout
-      - run: bash .circleci/merge_base_branch.sh
-      - run: POSTGRES=1 /synapse_sytest.sh
-      - store_artifacts:
-          path: /logs
-          destination: logs
-      - store_test_results:
-          path: /logs
 
   sytestpy3:
     docker:
@@ -126,14 +72,6 @@ workflows:
   version: 2
   build:
     jobs:
-      - sytestpy2:
-          filters:
-            branches:
-              only: /develop|master|release-.*/
-      - sytestpy2postgres:
-          filters:
-            branches:
-              only: /develop|master|release-.*/
       - sytestpy3:
           filters:
             branches:
@@ -142,14 +80,6 @@ workflows:
           filters:
             branches:
               only: /develop|master|release-.*/
-      - sytestpy2merged:
-          filters:
-            branches:
-              ignore: /develop|master|release-.*/
-      - sytestpy2postgresmerged:
-          filters:
-            branches:
-              ignore: /develop|master|release-.*/
       - sytestpy3merged:
           filters:
             branches:
diff --git a/changelog.d/5425.removal b/changelog.d/5425.removal
new file mode 100644
index 000000000..30022ee63
--- /dev/null
+++ b/changelog.d/5425.removal
@@ -0,0 +1 @@
+Python 2.7 is no longer a supported platform. Synapse now requires Python 3.5+ to run.
diff --git a/setup.py b/setup.py
index 55663e9ca..3492cdc5a 100755
--- a/setup.py
+++ b/setup.py
@@ -102,6 +102,16 @@ setup(
     include_package_data=True,
     zip_safe=False,
     long_description=long_description,
+    python_requires='~=3.5',
+    classifiers=[
+        'Development Status :: 5 - Production/Stable',
+        'Topic :: Communications :: Chat',
+        'License :: OSI Approved :: Apache Software License',
+        'Programming Language :: Python :: 3 :: Only',
+        'Programming Language :: Python :: 3.5',
+        'Programming Language :: Python :: 3.6',
+        'Programming Language :: Python :: 3.7',
+    ],
     scripts=["synctl"] + glob.glob("scripts/*"),
     cmdclass={'test': TestCommand},
 )
diff --git a/synapse/__init__.py b/synapse/__init__.py
index 5bc24863d..0c0154678 100644
--- a/synapse/__init__.py
+++ b/synapse/__init__.py
@@ -17,6 +17,13 @@
 """ This is a reference implementation of a Matrix home server.
 """
 
+import sys
+
+# Check that we're not running on an unsupported Python version.
+if sys.version_info < (3, 5):
+    print("Synapse requires Python 3.5 or above.")
+    sys.exit(1)
+
 try:
     from twisted.internet import protocol
     from twisted.internet.protocol import Factory
diff --git a/synapse/python_dependencies.py b/synapse/python_dependencies.py
index 7dfa78dad..11ace2bfb 100644
--- a/synapse/python_dependencies.py
+++ b/synapse/python_dependencies.py
@@ -44,7 +44,7 @@ REQUIREMENTS = [
     "canonicaljson>=1.1.3",
     "signedjson>=1.0.0",
     "pynacl>=1.2.1",
-    "idna>=2",
+    "idna>=2.5",
 
     # validating SSL certs for IP addresses requires service_identity 18.1.
     "service_identity>=18.1.0",
@@ -65,7 +65,7 @@ REQUIREMENTS = [
     "sortedcontainers>=1.4.4",
     "psutil>=2.0.0",
     "pymacaroons>=0.13.0",
-    "msgpack>=0.5.0",
+    "msgpack>=0.5.2",
     "phonenumbers>=8.2.0",
     "six>=1.10",
     # prometheus_client 0.4.0 changed the format of counter metrics
diff --git a/tox.ini b/tox.ini
index 543b232ae..0c4d56276 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = packaging, py27, py36, pep8, check_isort
+envlist = packaging, py35, py36, py37, pep8, check_isort
 
 [base]
 deps =
@@ -79,7 +79,7 @@ usedevelop=true
 
 # A test suite for the oldest supported versions of Python libraries, to catch
 # any uses of APIs not available in them.
-[testenv:py27-old]
+[testenv:py35-old]
 skip_install=True
 deps =
     # Old automat version for Twisted