diff --git a/.github/workflows/pythonbuild.yml b/.github/workflows/pythonbuild.yml
index a32810c2f1..ec7f611f9f 100644
--- a/.github/workflows/pythonbuild.yml
+++ b/.github/workflows/pythonbuild.yml
@@ -13,8 +13,6 @@ jobs:
     strategy:
       matrix:
         include:
-          - python-version: "3.6"
-            tox-env: py36-core
           - python-version: "3.7"
             tox-env: py37-core
           - python-version: "3.8"
@@ -82,8 +80,6 @@ jobs:
     strategy:
       matrix:
         include:
-          - python-version: "3.6"
-            tox-env: py36-postgres
           - python-version: "3.7"
             tox-env: py37-postgres
           - python-version: "3.8"
@@ -137,8 +133,6 @@ jobs:
     strategy:
       matrix:
         include:
-          - python-version: "3.6"
-            tox-env: py36-aws
           - python-version: "3.7"
             tox-env: py37-aws
           - python-version: "3.8"
@@ -152,9 +146,6 @@ jobs:
           - python-version: "3.12"
             tox-env: py312-aws
 
-          - python-version: "3.6"
-            tox-env: py36-unixsocket
-            OVERRIDE_SKIP_CI_TESTS: True
           - python-version: "3.7"
             tox-env: py37-unixsocket
             OVERRIDE_SKIP_CI_TESTS: True
@@ -174,8 +165,6 @@ jobs:
             tox-env: py312-unixsocket
             OVERRIDE_SKIP_CI_TESTS: True
 
-          - python-version: "3.6"
-            tox-env: py36-apache
           - python-version: "3.7"
             tox-env: py37-apache
           - python-version: "3.8"
@@ -189,8 +178,6 @@ jobs:
           - python-version: "3.12"
             tox-env: py312-apache
 
-          - python-version: "3.6"
-            tox-env: py36-azureblob
           - python-version: "3.7"
             tox-env: py37-azureblob
           - python-version: "3.8"
diff --git a/README.rst b/README.rst
index deaffe4dc0..5500aa5923 100644
--- a/README.rst
+++ b/README.rst
@@ -18,7 +18,7 @@
     :target: https://luigi.readthedocs.io/en/stable/?badge=stable
     :alt: Documentation Status
 
-Luigi is a Python (3.6, 3.7, 3.8, 3.9, 3.10, 3.11, 3.12 tested) package that helps you build complex
+Luigi is a Python (3.7, 3.8, 3.9, 3.10, 3.11, 3.12 tested) package that helps you build complex
 pipelines of batch jobs. It handles dependency resolution, workflow management,
 visualization, handling failures, command line integration, and much more.
 
diff --git a/doc/configuration.rst b/doc/configuration.rst
index c4b1fdbe0c..909a4fe81d 100644
--- a/doc/configuration.rst
+++ b/doc/configuration.rst
@@ -32,7 +32,7 @@ These files are meant for both the client and ``luigid``.
 If you decide to specify your own configuration you should make sure
 that both the client and ``luigid`` load it properly.
 
-.. _ConfigParser.read: https://docs.python.org/3.6/library/configparser.html#configparser.ConfigParser.read
+.. _ConfigParser.read: https://docs.python.org/3/library/configparser.html#configparser.ConfigParser.read
 
 The config file is broken into sections, each controlling a different part of the config.
 
diff --git a/setup.py b/setup.py
index e01d76018a..77305b82e6 100644
--- a/setup.py
+++ b/setup.py
@@ -37,7 +37,7 @@ def get_static_files(path):
 with open('README.rst') as fobj:
     long_description = "\n\n" + readme_note + "\n\n" + fobj.read()
 
-install_requires = ['python-dateutil>=2.7.5,<3', 'tenacity>=8,<9']
+install_requires = ['python-dateutil>=2.7.5,<3', 'tenacity>=8,<9', 'tornado>=5.0,<7']
 
 # Can't use python-daemon>=2.2.0 if on windows
 #     See https://pagure.io/python-daemon/issue/18
@@ -46,19 +46,6 @@ def get_static_files(path):
 else:
     install_requires.append('python-daemon')
 
-# Start from tornado 6, the minimum supported Python version is 3.5.2.
-if sys.version_info[:3] >= (3, 5, 2):
-    install_requires.append('tornado>=5.0,<7')
-else:
-    install_requires.append('tornado>=5.0,<6')
-
-# Note: To support older versions of setuptools, we're explicitly not
-#   using conditional syntax (i.e. 'enum34>1.1.0;python_version<"3.4"').
-#   This syntax is a problem for setuptools as recent as `20.1.1`,
-#   published Feb 16, 2016.
-if sys.version_info[:2] < (3, 4):
-    install_requires.append('enum34>1.1.0')
-
 if os.environ.get('READTHEDOCS', None) == 'True':
     # So that we can build documentation for luigi.db_task_history and luigi.contrib.sqla
     install_requires.append('sqlalchemy')
@@ -111,8 +98,6 @@ def get_static_files(path):
         'Intended Audience :: Developers',
         'Intended Audience :: System Administrators',
         'License :: OSI Approved :: Apache Software License',
-        'Programming Language :: Python :: 3.5',
-        'Programming Language :: Python :: 3.6',
         'Programming Language :: Python :: 3.7',
         'Programming Language :: Python :: 3.8',
         'Programming Language :: Python :: 3.9',
diff --git a/tox.ini b/tox.ini
index 0e3f3e0f5d..943c1342f0 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py{35,36,37,38,39,310,311,312}-{cdh,hdp,core,contrib,apache,aws,gcloud,postgres,unixsocket,azureblob,dropbox}, visualiser, docs, flake8
+envlist = py{37,38,39,310,311,312}-{cdh,hdp,core,contrib,apache,aws,gcloud,postgres,unixsocket,azureblob,dropbox}, visualiser, docs, flake8
 skipsdist = True
 
 [pytest]