diff --git a/appveyor.yml b/appveyor.yml
index 72f9d881d3..fae4516e5d 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -38,6 +38,18 @@ environment:
       TOX_ENV: "py36"
       TOX_ARGS: ""
 
+    - PYTHON: "C:\\Python37"
+      PYTHON_VERSION: "3.7.x"
+      PYTHON_ARCH: "32"
+      TOX_ENV: "py37"
+      TOX_ARGS: "tornado.test.websocket_test"
+
+    - PYTHON: "C:\\Python37-x64"
+      PYTHON_VERSION: "3.7.x"
+      PYTHON_ARCH: "64"
+      TOX_ENV: "py37"
+      TOX_ARGS: ""
+
 install:
   # Make sure the right python version is first on the PATH.
   - "SET PATH=%PYTHON%;%PYTHON%\\Scripts;%PATH%"
diff --git a/demos/blog/Dockerfile b/demos/blog/Dockerfile
index 6440449cc0..4e3c7250be 100644
--- a/demos/blog/Dockerfile
+++ b/demos/blog/Dockerfile
@@ -1,4 +1,4 @@
-FROM python:3.6
+FROM python:3.7
 
 EXPOSE 8888
 
diff --git a/setup.py b/setup.py
index 6fbb10a892..0db840d99c 100644
--- a/setup.py
+++ b/setup.py
@@ -188,6 +188,7 @@ def build_extension(self, ext):
         'Programming Language :: Python :: 3.4',
         'Programming Language :: Python :: 3.5',
         'Programming Language :: Python :: 3.6',
+        'Programming Language :: Python :: 3.7',
         'Programming Language :: Python :: Implementation :: CPython',
         'Programming Language :: Python :: Implementation :: PyPy',
     ],
diff --git a/tornado/test/autoreload_test.py b/tornado/test/autoreload_test.py
index 1ea5316799..5cbdc2ee13 100644
--- a/tornado/test/autoreload_test.py
+++ b/tornado/test/autoreload_test.py
@@ -100,7 +100,9 @@ def test_reload_wrapper_preservation(self):
             env=dict(os.environ, PYTHONPATH=pythonpath),
             universal_newlines=True)
 
-        for i in range(20):
+        # This timeout needs to be fairly generous for pypy due to jit
+        # warmup costs.
+        for i in range(40):
             if autoreload_proc.poll() is not None:
                 break
             time.sleep(0.1)
diff --git a/tornado/test/iostream_test.py b/tornado/test/iostream_test.py
index abdd6b99eb..51fbb02a99 100644
--- a/tornado/test/iostream_test.py
+++ b/tornado/test/iostream_test.py
@@ -1028,7 +1028,7 @@ def test_future_write(self):
         """
         # Run concurrent writers that will write enough bytes so as to
         # clog the socket buffer and accumulate bytes in our write buffer.
-        m, n = 10000, 1000
+        m, n = 5000, 1000
         nproducers = 10
         total_bytes = m * n * nproducers
         server, client = yield self.make_iostream_pair(max_buffer_size=total_bytes)
diff --git a/tox.ini b/tox.ini
index 003881ad79..d52898b40b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -15,8 +15,8 @@ envlist =
         # Basic configurations: Run the tests in both minimal installations
         # and with all optional dependencies.
         # (pypy3 doesn't have any optional deps yet)
-        {py27,pypy,py34,py35,py36,pypy3},
-        {py27,pypy,py34,py35,py36}-full,
+        {py27,pypy,py34,py35,py36,py37,pypy3},
+        {py27,pypy,py34,py35,py36,py37}-full,
 
         # Also run the tests with each possible replacement of a default
         # component.  Run each test on both python 2 and 3 where possible.
@@ -57,10 +57,11 @@ basepython =
            py34: python3.4
            py35: python3.5
            py36: python3.6
+           py37: python3.7
            pypy: pypy
            pypy3: pypy3
            py2: python2.7
-           py3: python3.6
+           py3: python3.7
 
 deps =
      # unittest2 doesn't add anything we need on 2.7+, but we should ensure that
@@ -69,12 +70,12 @@ deps =
      py3-unittest2: unittest2py3k
      # cpython-only deps: pycurl installs but curl_httpclient doesn't work;
      # twisted mostly works but is a bit flaky under pypy.
-     {py27,py34,py35,py36}-full: pycurl
+     {py27,py34,py35,py36,py37}-full: pycurl
      {py2,py3}: pycurl>=7.19.3.1
      # twisted is cpython only.
-     {py27,py34,py35,py36}-full: twisted
+     {py27,py34,py35,py36,py37}-full: twisted
      {py2,py3}: twisted
-     {py2,py3,py27,py34,py35,py36}-full: pycares
+     {py2,py3,py27,py34,py35,py36,py37}-full: pycares
      # mock became standard in py33
      {py2,py27,pypy,pypy3}-full: mock
      # singledispatch became standard in py34.
@@ -86,7 +87,7 @@ deps =
 
 setenv =
        # The extension is mandatory on cpython.
-       {py2,py27,py3,py34,py35,py36}: TORNADO_EXTENSION=1
+       {py2,py27,py3,py34,py35,py36,py37}: TORNADO_EXTENSION=1
        # In python 3, opening files in text mode uses a
        # system-dependent encoding by default.  Run the tests with "C"
        # (ascii) and "utf-8" locales to ensure we don't have hidden
@@ -95,7 +96,7 @@ setenv =
        lang_utf8: LANG=en_US.utf-8
        # tox's parser chokes if all the setenv entries are conditional.
        DUMMY=dummy
-       {py2,py27,py3,py34,py35,py36}-no-ext: TORNADO_EXTENSION=0
+       {py2,py27,py3,py34,py35,py36,py37}-no-ext: TORNADO_EXTENSION=0
 
 # All non-comment lines but the last must end in a backslash.
 # Tox filters line-by-line based on the environment name.
@@ -103,7 +104,7 @@ commands =
          python \
          # py3*: -b turns on an extra warning when calling
          # str(bytes), and -bb makes it an error.
-         {py3,py34,py35,py36,pypy3}: -bb \
+         {py3,py34,py35,py36,py37,pypy3}: -bb \
          # Python's optimized mode disables the assert statement, so
          # run the tests in this mode to ensure we haven't fallen into
          # the trap of relying on an assertion's side effects or using