diff --git a/.travis.yml b/.travis.yml
index 2e98cf47aea3e..93c8238bb5059 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -62,9 +62,6 @@ matrix:
     - arch: arm64
       env:
         - JOB="3.7, arm64" PYTEST_WORKERS=8 ENV_FILE="ci/deps/travis-37-arm64.yaml" PATTERN="(not slow and not network and not clipboard)"
-    - dist: bionic
-      env:
-        - JOB="3.9-dev" PATTERN="(not slow and not network and not clipboard)"
 
 
 before_install:
diff --git a/asv_bench/asv.conf.json b/asv_bench/asv.conf.json
index 1863a17e3d5f7..e8e82edabbfa3 100644
--- a/asv_bench/asv.conf.json
+++ b/asv_bench/asv.conf.json
@@ -39,7 +39,7 @@
     // followed by the pip installed packages).
     "matrix": {
         "numpy": [],
-        "Cython": ["0.29.16"],
+        "Cython": ["0.29.21"],
         "matplotlib": [],
         "sqlalchemy": [],
         "scipy": [],
diff --git a/ci/build39.sh b/ci/build39.sh
index b9c76635df99b..f2ef11d5a71f4 100755
--- a/ci/build39.sh
+++ b/ci/build39.sh
@@ -3,8 +3,7 @@
 
 sudo apt-get install build-essential gcc xvfb
 pip install --no-deps -U pip wheel setuptools
-pip install numpy python-dateutil pytz pytest pytest-xdist hypothesis
-pip install cython --pre # https://github.com/cython/cython/issues/3395
+pip install cython numpy python-dateutil pytz pytest pytest-xdist hypothesis
 
 python setup.py build_ext -inplace
 python -m pip install --no-build-isolation -e .
diff --git a/ci/deps/azure-37-32bit.yaml b/ci/deps/azure-37-32bit.yaml
index 8e0cd73a9536d..3cdd98485f281 100644
--- a/ci/deps/azure-37-32bit.yaml
+++ b/ci/deps/azure-37-32bit.yaml
@@ -21,6 +21,6 @@ dependencies:
   # see comment above
   - pip
   - pip:
-    - cython>=0.29.16
+    - cython>=0.29.21
     - numpy>=1.16.5
     - pytest>=5.0.1
diff --git a/ci/deps/azure-37-locale.yaml b/ci/deps/azure-37-locale.yaml
index cc996f4077cd9..64480258fe65e 100644
--- a/ci/deps/azure-37-locale.yaml
+++ b/ci/deps/azure-37-locale.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - pytest-asyncio
diff --git a/ci/deps/azure-37-locale_slow.yaml b/ci/deps/azure-37-locale_slow.yaml
index fbb1ea671d696..7f658fe62d268 100644
--- a/ci/deps/azure-37-locale_slow.yaml
+++ b/ci/deps/azure-37-locale_slow.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/azure-37-minimum_versions.yaml b/ci/deps/azure-37-minimum_versions.yaml
index 31f82f3304db3..afd5b07cc6654 100644
--- a/ci/deps/azure-37-minimum_versions.yaml
+++ b/ci/deps/azure-37-minimum_versions.yaml
@@ -5,7 +5,7 @@ dependencies:
   - python=3.7.1
 
   # tools
-  - cython=0.29.16
+  - cython=0.29.21
   - pytest=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/azure-37-slow.yaml b/ci/deps/azure-37-slow.yaml
index d17a8a2b0ed9b..13a0d442bcae7 100644
--- a/ci/deps/azure-37-slow.yaml
+++ b/ci/deps/azure-37-slow.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/azure-38-locale.yaml b/ci/deps/azure-38-locale.yaml
index bb40127b672d3..8ce58e07a8542 100644
--- a/ci/deps/azure-38-locale.yaml
+++ b/ci/deps/azure-38-locale.yaml
@@ -5,7 +5,7 @@ dependencies:
   - python=3.8.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - pytest-asyncio>=0.12.0
diff --git a/ci/deps/azure-38-numpydev.yaml b/ci/deps/azure-38-numpydev.yaml
index 37592086d49e3..274be0361c2e5 100644
--- a/ci/deps/azure-38-numpydev.yaml
+++ b/ci/deps/azure-38-numpydev.yaml
@@ -14,7 +14,7 @@ dependencies:
   - pytz
   - pip
   - pip:
-    - cython==0.29.16 # GH#34014
+    - cython==0.29.21 # GH#34014
     - "git+git://github.com/dateutil/dateutil.git"
     - "--extra-index-url https://pypi.anaconda.org/scipy-wheels-nightly/simple"
     - "--pre"
diff --git a/ci/deps/azure-macos-37.yaml b/ci/deps/azure-macos-37.yaml
index a5a69b9a59576..31e0ffca81424 100644
--- a/ci/deps/azure-macos-37.yaml
+++ b/ci/deps/azure-macos-37.yaml
@@ -31,6 +31,6 @@ dependencies:
   - xlwt
   - pip
   - pip:
-    - cython>=0.29.16
+    - cython>=0.29.21
     - pyreadstat
     - pyxlsb
diff --git a/ci/deps/azure-windows-37.yaml b/ci/deps/azure-windows-37.yaml
index 1d15ca41c0f8e..16b4bd72683b4 100644
--- a/ci/deps/azure-windows-37.yaml
+++ b/ci/deps/azure-windows-37.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/azure-windows-38.yaml b/ci/deps/azure-windows-38.yaml
index 23bede5eb26f1..449bbd05991bf 100644
--- a/ci/deps/azure-windows-38.yaml
+++ b/ci/deps/azure-windows-38.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.8.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/travis-37-arm64.yaml b/ci/deps/travis-37-arm64.yaml
index ea29cbef1272b..d04b1ca0bdcfc 100644
--- a/ci/deps/travis-37-arm64.yaml
+++ b/ci/deps/travis-37-arm64.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.13
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/travis-37-cov.yaml b/ci/deps/travis-37-cov.yaml
index 33ee6dfffb1a3..d031dc1cc062f 100644
--- a/ci/deps/travis-37-cov.yaml
+++ b/ci/deps/travis-37-cov.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/travis-37-locale.yaml b/ci/deps/travis-37-locale.yaml
index 306f74a0101e3..8a0b5b043ceca 100644
--- a/ci/deps/travis-37-locale.yaml
+++ b/ci/deps/travis-37-locale.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/travis-37.yaml b/ci/deps/travis-37.yaml
index 26d6c2910a7cc..6a15ce1195ea9 100644
--- a/ci/deps/travis-37.yaml
+++ b/ci/deps/travis-37.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.7.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/ci/deps/travis-38.yaml b/ci/deps/travis-38.yaml
index b879c0f81dab2..874c8dd96d008 100644
--- a/ci/deps/travis-38.yaml
+++ b/ci/deps/travis-38.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.8.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21
   - hypothesis>=3.58.0
diff --git a/doc/source/getting_started/install.rst b/doc/source/getting_started/install.rst
index fde9f567cc3ec..2196c908ecf37 100644
--- a/doc/source/getting_started/install.rst
+++ b/doc/source/getting_started/install.rst
@@ -18,7 +18,7 @@ Instructions for installing from source,
 Python version support
 ----------------------
 
-Officially Python 3.7.1 and above, and 3.8.
+Officially Python 3.7.1 and above, 3.8, and 3.9.
 
 Installing pandas
 -----------------
diff --git a/doc/source/whatsnew/v1.1.3.rst b/doc/source/whatsnew/v1.1.3.rst
index 8ead78a17e9c2..72526140b6eb8 100644
--- a/doc/source/whatsnew/v1.1.3.rst
+++ b/doc/source/whatsnew/v1.1.3.rst
@@ -10,6 +10,21 @@ including other versions of pandas.
 
 .. ---------------------------------------------------------------------------
 
+Enhancements
+~~~~~~~~~~~~
+
+Added support for new Python version
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Pandas 1.1.3 now supports Python 3.9 (:issue:`36296`).
+
+Development Changes
+^^^^^^^^^^^^^^^^^^^
+
+- The minimum version of Cython is now the most recent bug-fix version (0.29.21) (:issue:`36296`).
+
+.. ---------------------------------------------------------------------------
+
 .. _whatsnew_113.regressions:
 
 Fixed regressions
diff --git a/environment.yml b/environment.yml
index badb0ba94a670..36bbd3d307159 100644
--- a/environment.yml
+++ b/environment.yml
@@ -12,7 +12,7 @@ dependencies:
   - asv
 
   # building
-  - cython>=0.29.16
+  - cython>=0.29.21
 
   # code checks
   - black=19.10b0
diff --git a/pandas/_libs/writers.pyx b/pandas/_libs/writers.pyx
index 40c39aabb7a7a..f6823c3cb0d3f 100644
--- a/pandas/_libs/writers.pyx
+++ b/pandas/_libs/writers.pyx
@@ -1,11 +1,7 @@
 import cython
-from cython import Py_ssize_t
-
-from cpython.bytes cimport PyBytes_GET_SIZE
-from cpython.unicode cimport PyUnicode_GET_SIZE
-
 import numpy as np
 
+from cpython cimport PyBytes_GET_SIZE, PyUnicode_GET_LENGTH
 from numpy cimport ndarray, uint8_t
 
 ctypedef fused pandas_string:
@@ -144,7 +140,7 @@ cpdef inline Py_ssize_t word_len(object val):
         Py_ssize_t l = 0
 
     if isinstance(val, str):
-        l = PyUnicode_GET_SIZE(val)
+        l = PyUnicode_GET_LENGTH(val)
     elif isinstance(val, bytes):
         l = PyBytes_GET_SIZE(val)
 
diff --git a/pyproject.toml b/pyproject.toml
index f6f8081b6c464..8161e8ad752da 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,7 +4,7 @@
 requires = [
     "setuptools",
     "wheel",
-    "Cython>=0.29.16,<3",  # Note: sync with setup.py
+    "Cython>=0.29.21,<3",  # Note: sync with setup.py
     "numpy==1.16.5; python_version=='3.7' and platform_system!='AIX'",
     "numpy==1.17.3; python_version>='3.8' and platform_system!='AIX'",
     "numpy==1.16.5; python_version=='3.7' and platform_system=='AIX'",
diff --git a/requirements-dev.txt b/requirements-dev.txt
index c53ced35d27fa..fb647c10f72bc 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -5,7 +5,7 @@ numpy>=1.16.5
 python-dateutil>=2.7.3
 pytz
 asv
-cython>=0.29.16
+cython>=0.29.21
 black==19.10b0
 cpplint
 flake8<3.8.0
diff --git a/setup.py b/setup.py
index f6f0cd9aabc0e..a8dfeb0974195 100755
--- a/setup.py
+++ b/setup.py
@@ -34,7 +34,7 @@ def is_platform_mac():
 
 
 min_numpy_ver = "1.16.5"
-min_cython_ver = "0.29.16"  # note: sync with pyproject.toml
+min_cython_ver = "0.29.21"  # note: sync with pyproject.toml
 
 try:
     import Cython
@@ -199,6 +199,7 @@ def build_extensions(self):
     "Programming Language :: Python :: 3",
     "Programming Language :: Python :: 3.7",
     "Programming Language :: Python :: 3.8",
+    "Programming Language :: Python :: 3.9",
     "Programming Language :: Cython",
     "Topic :: Scientific/Engineering",
 ]