diff --git a/.travis.yml b/.travis.yml
index 954ca04d4c..d7e57422cb 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -17,11 +17,10 @@ matrix:
     - python: '3.6'
       env: TOXENV="flake8,flake8-docs"
 
-    - python: '3.5'
-      env: TOXENV="py35-linux"
-
-    - python: '3.6'
-      env: TOXENV="py36-linux"
+    - python: '3.8'
+      env:
+        - TOXENV="py38-linux"
+      dist: bionic
 
     - python: '3.7'
       env:
@@ -30,6 +29,9 @@ matrix:
       dist: xenial
       sudo: true
 
+    - python: '3.6'
+      env: TOXENV="py36-linux"
+
 
 install:
   - pip install tox
diff --git a/appveyor.yml b/appveyor.yml
index 2a95324668..f0936471cd 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -14,21 +14,23 @@ environment:
     TOX_PARALLEL_NO_SPINNER: 1
 
   matrix:
-    - PYTHON: "C:\\Python35-x64"
-      PYTHON_VERSION: "3.5.2"
+# Python 3.8 builds on Appveyor/Windows failing; commented-out for now pending resolution
+# see comment at <https://github.com/RaRe-Technologies/gensim/pull/2715#issuecomment-569457589>
+#    - PYTHON: "C:\\Python38-x64"
+#      PYTHON_VERSION: "3.8.1"
+#      PYTHON_ARCH: "64"
+#      TOXENV: "py38-win"
+
+    - PYTHON: "C:\\Python37-x64"
+      PYTHON_VERSION: "3.7.6"
       PYTHON_ARCH: "64"
-      TOXENV: "py35-win"
+      TOXENV: "py37-win"
 
     - PYTHON: "C:\\Python36-x64"
-      PYTHON_VERSION: "3.6.0"
+      PYTHON_VERSION: "3.6.10"
       PYTHON_ARCH: "64"
       TOXENV: "py36-win"
 
-    - PYTHON: "C:\\Python37-x64"
-      PYTHON_VERSION: "3.7.0"
-      PYTHON_ARCH: "64"
-      TOXENV: "py37-win"
-
 init:
   - "ECHO %PYTHON% %PYTHON_VERSION% %PYTHON_ARCH%"
   - "ECHO \"%APPVEYOR_SCHEDULED_BUILD%\""
@@ -50,9 +52,15 @@ install:
   - "powershell ./continuous_integration/appveyor/install.ps1"
   - "SET PATH=%PYTHON%;%PYTHON%\\Scripts;%PATH%"
   - "python -m pip install -U pip tox"
-  - "pip --version"
 
-  # Check that we have the expected version and architecture for Python
+  # next line only to demo that py3.8-on-Appveyor *could* install Cython from wheel just fine,
+  # despite mysterious following attempt/failure to build-and-use Cython on that one Appveyor config
+  # delete when py3.8-on-Appveyor starts working normally
+  # see comment at <https://github.com/RaRe-Technologies/gensim/pull/2715#issuecomment-569457589>
+  - "python -m pip install Cython==0.29.14 numpy==1.18.0"
+
+  # Check that we have the expected versions and architecture
+  - "pip --version"
   - "python --version"
   - "python -c \"import struct; print(struct.calcsize('P') * 8)\""
 
diff --git a/setup.py b/setup.py
index 4625790e56..5422a32ad9 100644
--- a/setup.py
+++ b/setup.py
@@ -321,7 +321,7 @@ def run(self):
 # to build with any sane version of Cython, so we should update this pin
 # periodically.
 #
-CYTHON_STR = 'Cython==0.29.3'
+CYTHON_STR = 'Cython==0.29.14'
 
 install_requires = [
     NUMPY_STR,
diff --git a/tox.ini b/tox.ini
index 0ad3749097..12c8aa692b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 minversion = 2.0
-envlist = {py35,py36,py37}-{win,linux}, flake8, docs, docs-upload, download-wheels, upload-wheels, test-pypi
+envlist = {py36,py37,py38}-{win,linux}, flake8, docs, docs-upload, download-wheels, upload-wheels, test-pypi
 skipsdist = True
 platform = linux: linux
            win: win64
@@ -64,7 +64,7 @@ commands = flake8-rst gensim/ docs/ {posargs}
 basepython = python3
 recreate = True
 
-deps = numpy==1.14.5
+deps = numpy
 commands = python setup.py build_ext --inplace