diff --git a/.travis.yml b/.travis.yml
index b016cf386098e..1e5ea21b0f2d9 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 4583fac85b776..3a9c251968a3e 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-36-32bit.yaml b/ci/deps/azure-36-32bit.yaml
index 15704cf0d5427..6deb10a408ca4 100644
--- a/ci/deps/azure-36-32bit.yaml
+++ b/ci/deps/azure-36-32bit.yaml
@@ -22,5 +22,5 @@ dependencies:
   # see comment above
   - pip
   - pip:
-    - cython>=0.29.16
+    - cython>=0.29.21
     - pytest>=5.0.1
diff --git a/ci/deps/azure-36-locale.yaml b/ci/deps/azure-36-locale.yaml
index 536bb6f899773..72a64332b65db 100644
--- a/ci/deps/azure-36-locale.yaml
+++ b/ci/deps/azure-36-locale.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.6.*
 
   # 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-36-locale_slow.yaml b/ci/deps/azure-36-locale_slow.yaml
index c086b3651afc3..0a151944cdceb 100644
--- a/ci/deps/azure-36-locale_slow.yaml
+++ b/ci/deps/azure-36-locale_slow.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.6.*
 
   # 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-36-minimum_versions.yaml b/ci/deps/azure-36-minimum_versions.yaml
index f5af7bcf36189..5dfde5fc89183 100644
--- a/ci/deps/azure-36-minimum_versions.yaml
+++ b/ci/deps/azure-36-minimum_versions.yaml
@@ -5,7 +5,7 @@ dependencies:
   - python=3.6.1
 
   # 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-36-slow.yaml b/ci/deps/azure-36-slow.yaml
index 87bad59fa4873..7dd2f44b21c79 100644
--- a/ci/deps/azure-36-slow.yaml
+++ b/ci/deps/azure-36-slow.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.6.*
 
   # 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-locale.yaml b/ci/deps/azure-37-locale.yaml
index 6f64c81f299d1..359f1055ec4d3 100644
--- a/ci/deps/azure-37-locale.yaml
+++ b/ci/deps/azure-37-locale.yaml
@@ -5,7 +5,7 @@ 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-numpydev.yaml b/ci/deps/azure-37-numpydev.yaml
index 5cb58756a6ac1..7248b1740058f 100644
--- a/ci/deps/azure-37-numpydev.yaml
+++ b/ci/deps/azure-37-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-36.yaml b/ci/deps/azure-macos-36.yaml
index eeea249a19ca1..e2e47fe16e34e 100644
--- a/ci/deps/azure-macos-36.yaml
+++ b/ci/deps/azure-macos-36.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-36.yaml b/ci/deps/azure-windows-36.yaml
index 21b4e86918f3b..04fc1d8816712 100644
--- a/ci/deps/azure-windows-36.yaml
+++ b/ci/deps/azure-windows-36.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.6.*
 
   # tools
-  - cython>=0.29.16
+  - cython>=0.29.21
   - pytest>=5.0.1
   - pytest-xdist>=1.21,<2.0.0 # GH 35737
   - hypothesis>=3.58.0
diff --git a/ci/deps/azure-windows-37.yaml b/ci/deps/azure-windows-37.yaml
index 4d134b43760fe..026d8e1d2844f 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,<2.0.0 # GH 35737
   - hypothesis>=3.58.0
diff --git a/ci/deps/travis-36-cov.yaml b/ci/deps/travis-36-cov.yaml
index 2457c04e67759..c380423c55f19 100644
--- a/ci/deps/travis-36-cov.yaml
+++ b/ci/deps/travis-36-cov.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.6.*
 
   # 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-36-locale.yaml b/ci/deps/travis-36-locale.yaml
index 8f7e29abc5f3b..21176054ae0d7 100644
--- a/ci/deps/travis-36-locale.yaml
+++ b/ci/deps/travis-36-locale.yaml
@@ -6,7 +6,7 @@ dependencies:
   - python=3.6.*
 
   # 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 5cb53489be225..dcea6b7bd32e8 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.yaml b/ci/deps/travis-37.yaml
index e896233aac63c..6ded5b73a5d95 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 b79a9cd872c47..de6bfa62d1e7e 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 3.6.1 and above, 3.7, and 3.8.
+Officially Python 3.6.1 and above, 3.7, 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 7f5340b7022ce..763b9c12f7617 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 9efb995e29497..2df55d7e02e1b 100644
--- a/environment.yml
+++ b/environment.yml
@@ -13,7 +13,7 @@ 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 f282f2a085000..098a38958b5cc 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==1.15.4; python_version=='3.6' and platform_system!='AIX'",
     "numpy==1.15.4; python_version=='3.7' and platform_system!='AIX'",
     "numpy==1.17.3; python_version>='3.8' and platform_system!='AIX'",
diff --git a/requirements-dev.txt b/requirements-dev.txt
index c0dd77cd73ddc..19bc904265ea4 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -5,7 +5,7 @@ numpy>=1.15,<1.19.0
 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 22da02360619e..5555592de45e0 100755
--- a/setup.py
+++ b/setup.py
@@ -34,7 +34,7 @@ def is_platform_mac():
 
 
 min_numpy_ver = "1.15.4"
-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
@@ -200,6 +200,7 @@ def build_extensions(self):
     "Programming Language :: Python :: 3.6",
     "Programming Language :: Python :: 3.7",
     "Programming Language :: Python :: 3.8",
+    "Programming Language :: Python :: 3.9",
     "Programming Language :: Cython",
     "Topic :: Scientific/Engineering",
 ]