diff --git a/.travis.yml b/.travis.yml
index 2263dce..63b1589 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -34,6 +34,10 @@ env:
     - STACK=heroku-18 TEST_CMD=test/run-deps
     - STACK=heroku-18 TEST_CMD=test/run-versions
     - STACK=heroku-18 TEST_CMD=test/run-features
+
+    - STACK=heroku-20 TEST_CMD=test/run-deps
+    - STACK=heroku-20 TEST_CMD=test/run-versions
+    - STACK=heroku-20 TEST_CMD=test/run-features
   global:
     - HATCHET_RETRIES=3
     - IS_RUNNING_ON_CI=true
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2554852..e5b4b0d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,7 @@
 
 ## Unreleased
 
+- Add support for Heroku-20 (#968).
 
 ## v182 (2020-10-06)
 
diff --git a/bin/steps/gdal b/bin/steps/gdal
index 6e3ff9f..6b0fa6f 100755
--- a/bin/steps/gdal
+++ b/bin/steps/gdal
@@ -21,8 +21,11 @@ source "$BIN_DIR/utils"
 # If GDAL exists within requirements, use vendored gdal.
 if (pip-grep -s requirements.txt GDAL gdal pygdal &> /dev/null) then
 
-  if [ ! -f ".heroku/vendor/bin/gdalserver" ]; then
+  if [[ ! -f ".heroku/vendor/bin/gdalserver" && "${STACK}" == 'heroku-20' ]]; then
+    puts-warn "The buildpack's built-in GDAL functonality is not supported on Heroku-20."
+    puts-warn "Please use this buildpack instead: https://github.com/heroku/heroku-geo-buildpack"
 
+  elif [[ ! -f ".heroku/vendor/bin/gdalserver" ]]; then
     puts-warn "The vendored GDAL package in the Heroku Python Buildpack now deprecated."
     puts-warn "To enable GDAL use an alternative buildpack is available here - https://github.com/heroku/heroku-geo-buildpack"
 
diff --git a/bin/steps/geo-libs b/bin/steps/geo-libs
index f3f88da..2e3a85a 100755
--- a/bin/steps/geo-libs
+++ b/bin/steps/geo-libs
@@ -20,8 +20,11 @@ PKG_CONFIG_PATH="/app/.heroku/vendor/lib/pkgconfig:$PKG_CONFIG_PATH"
 # shellcheck source=bin/utils
 source "$BIN_DIR/utils"
 
-# If GDAL exists within requirements, use vendored gdal.
-if [[ "$BUILD_WITH_GEO_LIBRARIES" ]]; then
+if [[ "$BUILD_WITH_GEO_LIBRARIES" && "${STACK}" == 'heroku-20' ]]; then
+  puts-warn "The GDAL, GEOS and PROJ binaries and BUILD_WITH_GEO_LIBRARIES functonality is not supported on Heroku-20."
+  puts-warn "Please use this buildpack for GDAL, GEOS and PROJ: https://github.com/heroku/heroku-geo-buildpack"
+  puts-warn "To hide this message, unset the BUILD_WITH_GEO_LIBRARIES variable using: heroku config:unset BUILD_WITH_GEO_LIBRARIES"
+elif [[ "$BUILD_WITH_GEO_LIBRARIES" ]]; then
   mcount "buildvar.BUILD_WITH_GEO_LIBRARIES"
 
   puts-warn "The GDAL, GEOS and PROJ binaries and BUILD_WITH_GEO_LIBRARIES functonality are now deprecated."
diff --git a/builds/heroku-20.Dockerfile b/builds/heroku-20.Dockerfile
new file mode 100644
index 0000000..4ee19ed
--- /dev/null
+++ b/builds/heroku-20.Dockerfile
@@ -0,0 +1,20 @@
+FROM heroku/heroku:20-build
+
+ENV WORKSPACE_DIR="/app/builds" \
+    S3_BUCKET="heroku-buildpack-python" \
+    S3_PREFIX="heroku-20/" \
+    STACK="heroku-20"
+
+RUN apt-get update \
+    && DEBIAN_FRONTEND=noninteractive apt-get install --no-install-recommends -y \
+        libsqlite3-dev \
+        python3-pip \
+        python3-setuptools \
+    && rm -rf /var/lib/apt/lists/*
+
+WORKDIR /app
+
+COPY requirements.txt /app/
+RUN pip3 install --disable-pip-version-check --no-cache-dir -r /app/requirements.txt
+
+COPY . /app
diff --git a/test/fixtures/pipenv-full-version/Pipfile b/test/fixtures/pipenv-full-version/Pipfile
index af6f4e4..c91c768 100644
--- a/test/fixtures/pipenv-full-version/Pipfile
+++ b/test/fixtures/pipenv-full-version/Pipfile
@@ -6,4 +6,4 @@ verify_ssl = true
 requests = "*"
 
 [requires]
-python_full_version = "3.6.3"
\ No newline at end of file
+python_full_version = "3.7.8"
diff --git a/test/fixtures/pipenv-full-version/Pipfile.lock b/test/fixtures/pipenv-full-version/Pipfile.lock
index 0a758bd..9f364d0 100644
--- a/test/fixtures/pipenv-full-version/Pipfile.lock
+++ b/test/fixtures/pipenv-full-version/Pipfile.lock
@@ -1,24 +1,11 @@
 {
     "_meta": {
         "hash": {
-            "sha256": "22a052f4d1cfe6518b2f236fe45c3208c587a9ab1323bdd390632e27278b541e"
-        },
-        "host-environment-markers": {
-            "implementation_name": "cpython",
-            "implementation_version": "3.6.3",
-            "os_name": "posix",
-            "platform_machine": "x86_64",
-            "platform_python_implementation": "CPython",
-            "platform_release": "16.7.0",
-            "platform_system": "Darwin",
-            "platform_version": "Darwin Kernel Version 16.7.0: Thu Jun 15 17:36:27 PDT 2017; root:xnu-3789.70.16~2/RELEASE_X86_64",
-            "python_full_version": "3.6.3",
-            "python_version": "3.6",
-            "sys_platform": "darwin"
+            "sha256": "8a36860f0f9cb55716222098062cea5c5e0f8127cafb9d0c694de327bac9fbc0"
         },
         "pipfile-spec": 6,
         "requires": {
-            "python_full_version": "3.6.3"
+            "python_full_version": "3.7.8"
         },
         "sources": [
             {
diff --git a/test/fixtures/python3_6_warn/runtime.txt b/test/fixtures/python3_6_warn/runtime.txt
index 34b35b7..a06518f 100644
--- a/test/fixtures/python3_6_warn/runtime.txt
+++ b/test/fixtures/python3_6_warn/runtime.txt
@@ -1 +1 @@
-python-3.6.7
+python-3.6.11
diff --git a/test/fixtures/python3_7_warn/runtime.txt b/test/fixtures/python3_7_warn/runtime.txt
index 4255f73..32a8d83 100644
--- a/test/fixtures/python3_7_warn/runtime.txt
+++ b/test/fixtures/python3_7_warn/runtime.txt
@@ -1 +1 @@
-python-3.7.1
+python-3.7.8
diff --git a/test/fixtures/python3_8_warn/runtime.txt b/test/fixtures/python3_8_warn/runtime.txt
index 73b1cf8..43b47fb 100644
--- a/test/fixtures/python3_8_warn/runtime.txt
+++ b/test/fixtures/python3_8_warn/runtime.txt
@@ -1 +1 @@
-python-3.8.0
+python-3.8.5
diff --git a/test/run-deps b/test/run-deps
index 8b69f2a..beb87f6 100755
--- a/test/run-deps
+++ b/test/run-deps
@@ -21,16 +21,13 @@ testGEOS() {
   local env_dir="$(mktmpdir)"
   echo '1' > "${env_dir}/BUILD_WITH_GEO_LIBRARIES"
   compile 'geos' '' "${env_dir}"
-  assertCaptured "geos"
-  assertCapturedSuccess
-}
-
-testGEOSDeprecation() {
-  local env_dir="$(mktmpdir)"
-  echo '1' > "${env_dir}/BUILD_WITH_GEO_LIBRARIES"
-  compile 'geos' '' "${env_dir}"
-  assertCaptured " !     The GDAL, GEOS and PROJ binaries and BUILD_WITH_GEO_LIBRARIES functonality are now deprecated.
- !     An alternative buildpack to enable GDAL, GEOS and PROJ use is available here - https://github.com/heroku/heroku-geo-buildpack"
+  if [[ $STACK == "heroku-20" ]]; then
+    assertCaptured " !     The GDAL, GEOS and PROJ binaries and BUILD_WITH_GEO_LIBRARIES functonality is not supported on Heroku-20."
+  else
+    assertCaptured " !     The GDAL, GEOS and PROJ binaries and BUILD_WITH_GEO_LIBRARIES functonality are now deprecated."
+  fi
+  # This should assertCapturedError on Heroku-20, but the test doesn't actually
+  # install anything that uses GEOS so succeeds (see W-8145375)
   assertCapturedSuccess
 }
 
@@ -55,6 +52,11 @@ testPsycopg2() {
 }
 
 testPysqlite() {
+  # pysqlite does not support Python 3 (since the sqlite3 stdlib can be used there),
+  # so we have to test with Python 2, which we've not made available for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "pysqlite"
   assertCaptured "pysqlite"
   assertCapturedSuccess
diff --git a/test/run-features b/test/run-features
index f67da7b..a873788 100755
--- a/test/run-features
+++ b/test/run-features
@@ -68,6 +68,10 @@ testPipenvPythonVersion3_6() {
 }
 
 testPipenvPythonVersion2_7() {
+  # Python 2.7 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "pipenv-version2"
   assertCaptured "Installing ${LATEST_27}"
   # Can't use `assertCapturedSuccess` since stderr contains:
@@ -76,8 +80,12 @@ testPipenvPythonVersion2_7() {
 }
 
 testPipenvPythonFullVersion() {
+  # Python 3.7+ requires newer libssl than is present on Cedar-14.
+  if [[ "${STACK}" = "cedar-14" ]]; then
+    return
+  fi
   compile "pipenv-full-version"
-  assertCaptured "3.6.3"
+  assertCaptured "3.7.8"
   # Can't use `assertCapturedSuccess` since stderr contains:
   # "cp: cannot stat '/tmp/build_*/requirements.txt': No such file or directory" (W-7924941)
   assertCapturedSuccessWithStdErr
diff --git a/test/run-versions b/test/run-versions
index 15b6e99..63d2751 100755
--- a/test/run-versions
+++ b/test/run-versions
@@ -14,6 +14,10 @@ testPythonVersionUnspecified() {
 }
 
 testPython2_7() {
+  # Python 2.7 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "python2"
   assertCaptured "Installing ${LATEST_27}"
   assertCaptured "python-2-7-eol-faq";
@@ -24,6 +28,10 @@ testPython2_7() {
 }
 
 testPython2_7_warn() {
+  # Python 2.7 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "python2_warn"
   assertCaptured "Installing python-2.7.15"
   assertCaptured "python-2-7-eol-faq";
@@ -33,6 +41,10 @@ testPython2_7_warn() {
 }
 
 testPython3_4() {
+  # Python 3.4 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "python3_4"
   assertCaptured "Installing ${LATEST_34}"
   assertNotCaptured "security update"
@@ -44,6 +56,10 @@ testPython3_4() {
 }
 
 testPython3_4_warn() {
+  # Python 3.4 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "python3_4_warn"
   assertCaptured "Installing python-3.4.9"
   assertCaptured "security update!"
@@ -54,6 +70,10 @@ testPython3_4_warn() {
 }
 
 testPython3_5() {
+  # Python 3.5 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "python3_5"
   assertCaptured "Installing ${LATEST_35}"
   assertNotCaptured "security update"
@@ -63,6 +83,10 @@ testPython3_5() {
 }
 
 testPython3_5_warn() {
+  # Python 3.5 is EOL, so it has not been built for Heroku-20.
+  if [[ $STACK == "heroku-20" ]]; then
+    return
+  fi
   compile "python3_5_warn"
   assertCaptured "Installing python-3.5.6"
   assertCaptured "security update!"
@@ -81,7 +105,7 @@ testPython3_6() {
 
 testPython3_6_warn() {
   compile "python3_6_warn"
-  assertCaptured "Installing python-3.6.7"
+  assertCaptured "Installing python-3.6.11"
   assertCaptured "security update!"
   assertCaptured "${LATEST_36}"
   assertCapturedSuccess
@@ -106,7 +130,7 @@ testPython3_7_warn() {
     return
   fi
   compile "python3_7_warn"
-  assertCaptured "Installing python-3.7.1"
+  assertCaptured "Installing python-3.7.8"
   assertCaptured "security update!"
   assertCaptured "${LATEST_37}"
   assertCapturedSuccess
@@ -131,7 +155,7 @@ testPython3_8_warn() {
     return
   fi
   compile "python3_8_warn"
-  assertCaptured "Installing python-3.8.0"
+  assertCaptured "Installing python-3.8.5"
   assertCaptured "security update!"
   assertCaptured "${LATEST_38}"
   assertCapturedSuccess
@@ -208,7 +232,7 @@ testPypy2_7_warn() {
 testStickyPythonVersion() {
   local cache_dir="$(mktmpdir)"
   compile "python3_6_warn" "$cache_dir"
-  assertCaptured "Installing python-3.6.7"
+  assertCaptured "Installing python-3.6.11"
   assertCapturedSuccess
   compile "python_version_unspecified" "$cache_dir"
   assertNotCaptured "Installing python"
@@ -217,16 +241,16 @@ testStickyPythonVersion() {
   # Whilst this file seems like an implementation detail (so something that should
   # not be tested), we must guarantee the filename remains consistent for backwards
   # compatibility across buildpack versions for already-built apps.
-  assertFile "python-3.6.7" ".heroku/python-version"
+  assertFile "python-3.6.11" ".heroku/python-version"
 }
 
 testPythonVersionChange() {
   local cache_dir="$(mktmpdir)"
   compile "python3_6_warn" "$cache_dir"
-  assertCaptured "Installing python-3.6.7"
+  assertCaptured "Installing python-3.6.11"
   assertCapturedSuccess
   compile "python3_6" "$cache_dir"
-  assertCaptured "Found python-3.6.7, removing"
+  assertCaptured "Found python-3.6.11, removing"
   assertCapturedSuccess
 }