diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
new file mode 100644
index 0000000..9d75fb5
--- /dev/null
+++ b/.github/workflows/ci.yml
@@ -0,0 +1,69 @@
+name: Test
+
+on: [push, pull_request]
+
+jobs:
+  build:
+    name: Python ${{ matrix.python-version }}
+    runs-on: ${{ matrix.os }}
+    continue-on-error: ${{ matrix.experimental }}
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version:
+          - '2.7'
+          - '3.5'
+          - '3.6'
+          - '3.7'
+          - '3.8'
+          - '3.9'
+        experimental:
+          - false
+        os: [ubuntu-latest]
+        include:
+          # Python 3.4 is not on ubuntu-latest
+          - python-version: '3.4'
+            os: ubuntu-18.04
+            experimental: false
+
+          # Python 3.10 is currently failing, but this may be OK
+          - python-version: '3.10.0-alpha - 3.10'
+            os: ubuntu-latest
+            experimental: true
+
+    steps:
+      - uses: actions/checkout@v2
+
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v2
+        with:
+          python-version: ${{ matrix.python-version }}
+
+      - uses: actions/cache@v2
+        with:
+          path: ~/.cache/pip
+          key: ${{ runner.os }}-pip-${{ hashFiles('**/requirements.txt') }}
+          restore-keys: |
+            ${{ runner.os }}-pip-
+
+      - name: Install dependencies
+        id: install
+        run: |
+          set -x
+          pip install -r requirements.txt
+
+          # install mypy on Python 3.6+
+          if python -c \
+              'import sys; sys.exit(0 if sys.version_info >= (3, 6) else 1)'; then
+            pip install -U mypy
+            echo "::set-output name=mypy::true"
+          fi
+
+      - name: Run pytest
+        run: |
+          pytest
+
+      - name: Run mypy
+        if: ${{ steps.install.outputs.mypy }}
+        run: |
+          mypy pyannotate_*
diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index 3456990..0000000
--- a/.travis.yml
+++ /dev/null
@@ -1,28 +0,0 @@
-language: python
-cache: pip
-matrix:
-    include:
-        - python: '2.7'
-        - python: '3.4'
-        - python: '3.5.1'     # Special, it doesn't have typing.Text
-          dist: trusty        # needed because xenial doesn't have 3.5.1
-        - python: '3.5'       # Latest, e.g. 3.5.4
-        - python: '3.6'
-          env: USE_MYPY=true
-        - python: '3.7'
-          dist: xenial        # needed because Python 3.7 is broken on travis CI Trusty
-          sudo: true
-          env: USE_MYPY=true
-        - python: '3.8-dev'
-          dist: xenial        # needed because Python 3.8 is broken on travis CI Trusty
-          sudo: true
-          env: USE_MYPY=true
-    allow_failures:
-        - python: 3.8-dev
-  
-install:
-    - pip install -r requirements.txt
-    - if [[ $USE_MYPY == true ]]; then pip install -U mypy; fi
-script:
-    - pytest
-    - if [[ $USE_MYPY == true ]]; then mypy pyannotate_*; fi
diff --git a/pyannotate_tools/fixes/tests/test_annotate_json_py3.py b/pyannotate_tools/fixes/tests/test_annotate_json_py3.py
index 09212be..9960d25 100644
--- a/pyannotate_tools/fixes/tests/test_annotate_json_py3.py
+++ b/pyannotate_tools/fixes/tests/test_annotate_json_py3.py
@@ -6,7 +6,11 @@
 import tempfile
 import unittest
 import sys
-from mock import patch
+
+try:
+    from unittest.mock import patch
+except ImportError:
+    from mock import patch  # type: ignore
 
 from lib2to3.tests.test_fixers import FixerTestCase
 
diff --git a/requirements.txt b/requirements.txt
index ffaffbd..da8a727 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,13 @@
+mock; python_version < '3.3'
 mypy_extensions>=0.3.0
-pytest>=3.3.0
+pytest>=3.3.0; python_version > '3.5'
+# pytest >5.3.0 uses typing.Type from Python 3.5.2
+pytest>=3.3.0,<=5.3.0; python_version <= '3.5'
+# importlib-metadata is needed for Python 3.5+, but pip does not seem to be
+# pinning it to a correct version for Python 3.5 (possibly because it's a
+# transitive dependency).
+# Python 3.5 support was dropped in importlib-metadata 3.0.0
+importlib-metadata>=0.12,<3.0.0; python_version == '3.5'
 setuptools>=28.8.0
 six>=1.11.0
 typing>=3.6.2; python_version < '3.5'