diff --git a/.travis.yml b/.travis.yml
index f6c91c262..d88f10324 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,4 +1,4 @@
-sudo: false
+dist: xenial
 language: python
 
 cache:
@@ -54,23 +54,23 @@ matrix:
     python: 3.5
     env: TOX_ENV=py35,codecov TRIAL_FLAGS="-j 2"
 
-  - name: "py3.6 / sqlite"
-    python: 3.6
-    env: TOX_ENV=py36,codecov TRIAL_FLAGS="-j 2"
+  - name: "py3.7 / sqlite"
+    python: 3.7
+    env: TOX_ENV=py37,codecov TRIAL_FLAGS="-j 2"
 
-  - name: "py3.6 / postgres9.4"
-    python: 3.6
+  - name: "py3.7 / postgres9.4"
+    python: 3.7
     addons:
       postgresql: "9.4"
-    env: TOX_ENV=py36-postgres TRIAL_FLAGS="-j 4"
+    env: TOX_ENV=py37-postgres TRIAL_FLAGS="-j 4"
     services:
       - postgresql
 
-  - name: "py3.6 / postgres9.5"
-    python: 3.6
+  - name: "py3.7 / postgres9.5"
+    python: 3.7
     addons:
       postgresql: "9.5"
-    env: TOX_ENV=py36-postgres,codecov TRIAL_FLAGS="-j 4"
+    env: TOX_ENV=py37-postgres,codecov TRIAL_FLAGS="-j 4"
     services:
       - postgresql
 
@@ -86,7 +86,7 @@ matrix:
 
 install:
   # this just logs the postgres version we will be testing against (if any)
-  - psql -At -U postgres -c 'select version();'
+  - psql -At -U postgres -c 'select version();' || true
 
   - pip install tox
   
diff --git a/changelog.d/4677.misc b/changelog.d/4677.misc
new file mode 100644
index 000000000..6f4596be4
--- /dev/null
+++ b/changelog.d/4677.misc
@@ -0,0 +1 @@
+Run unit tests against python 3.7.
diff --git a/tox.ini b/tox.ini
index 3e2dba292..14437e733 100644
--- a/tox.ini
+++ b/tox.ini
@@ -3,7 +3,6 @@ envlist = packaging, py27, py36, pep8, check_isort
 
 [base]
 deps =
-    Twisted>=17.1
     mock
     python-subunit
     junitxml
@@ -38,6 +37,7 @@ whitelist_externals =
 
 setenv =
     {[base]setenv}
+    postgres: SYNAPSE_POSTGRES = 1
 
 passenv = *
 
@@ -47,8 +47,6 @@ commands =
     sh -c 'echo "import coverage; coverage.process_startup()" > {envsitepackagesdir}/../sitecustomize.py'
     {envbindir}/coverage run "{envbindir}/trial" {env:TRIAL_FLAGS:} {posargs:tests} {env:TOXSUFFIX:}
 
-[testenv:py27]
-
 # As of twisted 16.4, trial tries to import the tests as a package (previously
 # it loaded the files explicitly), which means they need to be on the
 # pythonpath. Our sdist doesn't include the 'tests' package, so normally it
@@ -72,14 +70,7 @@ commands =
 # )
 usedevelop=true
 
-[testenv:py27-postgres]
-usedevelop=true
-deps =
-    {[base]deps}
-    psycopg2
-setenv =
-    {[base]setenv}
-    SYNAPSE_POSTGRES = 1
+
 
 # A test suite for the oldest supported versions of Python libraries, to catch
 # any uses of APIs not available in them.
@@ -101,22 +92,6 @@ commands =
     pip install -e .
     {envbindir}/trial {env:TRIAL_FLAGS:} {posargs:tests} {env:TOXSUFFIX:}
 
-[testenv:py35]
-usedevelop=true
-
-[testenv:py36]
-usedevelop=true
-
-[testenv:py36-postgres]
-usedevelop=true
-deps =
-    {[base]deps}
-    psycopg2
-setenv =
-    {[base]setenv}
-    SYNAPSE_POSTGRES = 1
-
-
 [testenv:packaging]
 skip_install=True
 deps =