diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 8cbd8629..f4149430 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -42,6 +42,8 @@ jobs:
             tox_env: py38-full
           - python: '3.9'
             tox_env: py39-full
+          - python: '3.10'
+            tox_env: py310-full
           - python: 'pypy-3.8'
             # Pypy is a lot slower due to jit warmup costs, so don't run the
             # "full" test config there.
diff --git a/docs/index.rst b/docs/index.rst
index 6f59bd70..7877be8c 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -96,7 +96,7 @@ installed in this way, so you may wish to download a copy of the
 source tarball or clone the `git repository
 <https://github.com/tornadoweb/tornado>`_ as well.
 
-**Prerequisites**: Tornado 6.0 requires Python 3.6 or newer (See
+**Prerequisites**: Tornado 6.0 requires Python 3.7 or newer (See
 `Tornado 5.1 <https://www.tornadoweb.org/en/branch5.1/>`_ if
 compatibility with Python 2.7 is required). The following optional
 packages may be useful:
diff --git a/pyproject.toml b/pyproject.toml
index 73200f4f..29e9dab6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,5 +1,5 @@
 [tool.cibuildwheel]
-build = "cp3[789]*"
+build = "cp3[789]* cp310*"
 test-command = "python -m tornado.test"
 
 [tool.cibuildwheel.macos]
diff --git a/setup.cfg b/setup.cfg
index a365d2c3..e8bf8067 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -2,7 +2,7 @@
 license_file = LICENSE
 
 [mypy]
-python_version = 3.6
+python_version = 3.7
 no_implicit_optional = True
 
 [mypy-tornado.*,tornado.platform.*]
diff --git a/setup.py b/setup.py
index 7c9b35c5..3f82314d 100644
--- a/setup.py
+++ b/setup.py
@@ -138,7 +138,7 @@ if (
 
 
 if setuptools is not None:
-    python_requires = ">= 3.6"
+    python_requires = ">= 3.7"
     kwargs["python_requires"] = python_requires
 
 setup(
@@ -180,10 +180,10 @@ setup(
     classifiers=[
         "License :: OSI Approved :: Apache Software License",
         "Programming Language :: Python :: 3",
-        "Programming Language :: Python :: 3.6",
         "Programming Language :: Python :: 3.7",
         "Programming Language :: Python :: 3.8",
         "Programming Language :: Python :: 3.9",
+        "Programming Language :: Python :: 3.10",
         "Programming Language :: Python :: Implementation :: CPython",
         "Programming Language :: Python :: Implementation :: PyPy",
     ],
diff --git a/tornado/test/process_test.py b/tornado/test/process_test.py
index 6ff8efde..ab290085 100644
--- a/tornado/test/process_test.py
+++ b/tornado/test/process_test.py
@@ -76,15 +76,15 @@ class ProcessTest(unittest.TestCase):
                 sock.close()
                 return
             try:
-                if asyncio is not None:
-                    # Reset the global asyncio event loop, which was put into
-                    # a broken state by the fork.
-                    asyncio.set_event_loop(asyncio.new_event_loop())
                 if id in (0, 1):
                     self.assertEqual(id, task_id())
-                    server = HTTPServer(self.get_app())
-                    server.add_sockets([sock])
-                    IOLoop.current().start()
+
+                    async def f():
+                        server = HTTPServer(self.get_app())
+                        server.add_sockets([sock])
+                        await asyncio.Event().wait()
+
+                    asyncio.run(f())
                 elif id == 2:
                     self.assertEqual(id, task_id())
                     sock.close()
diff --git a/tornado/testing.py b/tornado/testing.py
index 45e72c8b..088530cb 100644
--- a/tornado/testing.py
+++ b/tornado/testing.py
@@ -248,7 +248,7 @@ class AsyncTestCase(unittest.TestCase):
             tasks = asyncio.Task.all_tasks(asyncio_loop)
         # Tasks that are done may still appear here and may contain
         # non-cancellation exceptions, so filter them out.
-        tasks = [t for t in tasks if not t.done()]
+        tasks = [t for t in tasks if not t.done()]  # type: ignore
         for t in tasks:
             t.cancel()
         # Allow the tasks to run and finalize themselves (which means
diff --git a/tox.ini b/tox.ini
index 6c267598..56e01a81 100644
--- a/tox.ini
+++ b/tox.ini
@@ -13,7 +13,7 @@
 [tox]
 envlist =
         # Basic configurations: Run the tests for each python version.
-        py36-full,py37-full,py38-full,py39-full,pypy3-full
+        py37-full,py38-full,py39-full,py310-full,pypy3-full
 
         # Build and test the docs with sphinx.
         docs
@@ -27,10 +27,10 @@ whitelist_externals = /bin/sh
 [testenv]
 basepython =
            py3: python3
-           py36: python3.6
            py37: python3.7
            py38: python3.8
            py39: python3.9
+           py310: python3.10
            pypy3: pypy3
            # In theory, it doesn't matter which python version is used here.
            # In practice, things like changes to the ast module can alter
@@ -49,7 +49,7 @@ deps =
 
 setenv =
        # Treat the extension as mandatory in testing (but not on pypy)
-       {py3,py36,py37,py38,py39}: TORNADO_EXTENSION=1
+       {py3,py37,py38,py39,py310}: TORNADO_EXTENSION=1
        # CI workers are often overloaded and can cause our tests to exceed
        # the default timeout of 5s.
        ASYNC_TEST_TIMEOUT=25
@@ -61,7 +61,7 @@ setenv =
        # during sdist installation (and it doesn't seem to be
        # possible to set environment variables during that phase of
        # tox).
-       {py3,py36,py37,py38,py39,pypy3}: PYTHONWARNINGS=error:::tornado
+       {py3,py37,py38,py39,py310,pypy3}: PYTHONWARNINGS=error:::tornado
 
 
 # All non-comment lines but the last must end in a backslash.