diff --git a/.appveyor.yml b/.appveyor.yml
index 5df681cda..220bcea89 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -3,28 +3,28 @@ environment:
       PYTHON: "C:\\Python36"
 
     matrix:
-        - TOXENV: py27-pip20.0-coverage
-          PIP: 20.0
+        - TOXENV: py27-pip20.1-coverage
+          PIP: 20.1
         - TOXENV: py27-piplatest-coverage
           PIP: latest
 
-        - TOXENV: py35-pip20.0
-          PIP: 20.0
+        - TOXENV: py35-pip20.1
+          PIP: 20.1
         - TOXENV: py35-piplatest
           PIP: latest
 
-        - TOXENV: py36-pip20.0
-          PIP: 20.0
+        - TOXENV: py36-pip20.1
+          PIP: 20.1
         - TOXENV: py36-piplatest
           PIP: latest
 
-        - TOXENV: py37-pip20.0
-          PIP: 20.0
+        - TOXENV: py37-pip20.1
+          PIP: 20.1
         - TOXENV: py37-piplatest
           PIP: latest
 
-        - TOXENV: py38-pip20.0-coverage
-          PIP: 20.0
+        - TOXENV: py38-pip20.1-coverage
+          PIP: 20.1
         - TOXENV: py38-piplatest-coverage
           PIP: latest
 
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index b5da29dde..468375c63 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -28,8 +28,7 @@ jobs:
           - 3.7
         pip-version:
           - "latest"
-          - "20.2"  # TODO: update to 20.1 after pip-20.2 being released
-          - "20.0"
+          - "20.1"
         include:
           - os: Ubuntu
             python-version: 3.9-dev
diff --git a/.travis.yml b/.travis.yml
index 7ed071a83..44ab4a13d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,8 +11,7 @@ python:
 env:
   # NOTE: keep this in sync with envlist in tox.ini for tox-travis.
   - PIP=latest
-  - PIP=20.2  # TODO: update to 20.1 after pip-20.2 being released
-  - PIP=20.0
+  - PIP=20.1
 
 cache: false
 install:
diff --git a/README.rst b/README.rst
index 8f045a989..314eeaf2c 100644
--- a/README.rst
+++ b/README.rst
@@ -457,10 +457,12 @@ Versions and compatibility
 The table below summarizes the latest ``pip-tools`` versions with the required ``pip``
 versions.
 
-+-----------+-----------------+
-| pip-tools | pip             |
-+===========+=================+
-| 4.5.x     | 8.1.3 - 20.0.x  |
-+-----------+-----------------+
-| 5.x       | 20.0.x - 20.1.x |
-+-----------+-----------------+
++---------------+-----------------+
+| pip-tools     | pip             |
++===============+=================+
+| 4.5.*         | 8.1.3 - 20.0.2  |
++---------------+-----------------+
+| 5.0.0 - 5.3.0 | 20.0 - 20.1.1   |
++---------------+-----------------+
+| >= 5.4.0      | 20.1 - 20.2.*   |
++---------------+-----------------+
diff --git a/piptools/_compat/__init__.py b/piptools/_compat/__init__.py
index f67f0949a..fda80d571 100644
--- a/piptools/_compat/__init__.py
+++ b/piptools/_compat/__init__.py
@@ -4,7 +4,7 @@
 
 import six
 
-from .pip_compat import BAR_TYPES, PIP_VERSION, parse_requirements
+from .pip_compat import PIP_VERSION, parse_requirements
 
 if six.PY2:
     from .tempfile import TemporaryDirectory
diff --git a/piptools/_compat/pip_compat.py b/piptools/_compat/pip_compat.py
index 543593ad9..6cd24a0ff 100644
--- a/piptools/_compat/pip_compat.py
+++ b/piptools/_compat/pip_compat.py
@@ -3,23 +3,12 @@
 
 import pip
 from pip._internal.req import parse_requirements as _parse_requirements
+from pip._internal.req.constructors import install_req_from_parsed_requirement
 from pip._vendor.packaging.version import parse as parse_version
 
 PIP_VERSION = tuple(map(int, parse_version(pip.__version__).base_version.split(".")))
 
 
-if PIP_VERSION[:2] <= (20, 0):
-
-    def install_req_from_parsed_requirement(req, **kwargs):
-        return req
-
-    from pip._internal.utils.ui import BAR_TYPES
-
-else:
-    from pip._internal.req.constructors import install_req_from_parsed_requirement
-    from pip._internal.cli.progress_bars import BAR_TYPES
-
-
 def parse_requirements(
     filename, session, finder=None, options=None, constraint=False, isolated=False
 ):
diff --git a/piptools/repositories/local.py b/piptools/repositories/local.py
index 6c91d1b4f..473db096a 100644
--- a/piptools/repositories/local.py
+++ b/piptools/repositories/local.py
@@ -5,7 +5,6 @@
 
 from pip._internal.utils.hashes import FAVORITE_HASH
 
-from .._compat import PIP_VERSION
 from .base import BaseRepository
 
 from piptools.utils import as_tuple, key_from_ireq, make_install_requirement
@@ -79,10 +78,7 @@ def get_hashes(self, ireq):
             key_from_ireq(ireq)
         )
         if existing_pin and ireq_satisfied_by_existing_pin(ireq, existing_pin):
-            if PIP_VERSION[:2] <= (20, 0):
-                hashes = existing_pin.options.get("hashes", {})
-            else:
-                hashes = existing_pin.hash_options
+            hashes = existing_pin.hash_options
             hexdigests = hashes.get(FAVORITE_HASH)
             if hexdigests:
                 return {
diff --git a/piptools/repositories/pypi.py b/piptools/repositories/pypi.py
index 7480b5e85..261ffcd3f 100644
--- a/piptools/repositories/pypi.py
+++ b/piptools/repositories/pypi.py
@@ -10,6 +10,7 @@
 from shutil import rmtree
 
 from pip._internal.cache import WheelCache
+from pip._internal.cli.progress_bars import BAR_TYPES
 from pip._internal.commands import create_command
 from pip._internal.models.index import PackageIndex, PyPI
 from pip._internal.models.link import Link
@@ -23,7 +24,7 @@
 from pip._internal.utils.urls import path_to_url, url_to_path
 from pip._vendor.requests import RequestException
 
-from .._compat import BAR_TYPES, PIP_VERSION, TemporaryDirectory, contextlib
+from .._compat import PIP_VERSION, TemporaryDirectory, contextlib
 from ..click import progressbar
 from ..exceptions import NoCandidateFound
 from ..logging import log
@@ -187,9 +188,6 @@ def resolve_reqs(self, download_dir, ireq, wheel_cache):
                 # the ireq a name:
                 resolver._get_abstract_dist_for(ireq)
 
-            if PIP_VERSION[:2] <= (20, 0):
-                reqset.cleanup_files()
-
         return set(results)
 
     def get_dependencies(self, ireq):
@@ -238,9 +236,6 @@ def get_dependencies(self, ireq):
                         else:
                             del os.environ["PIP_REQ_TRACKER"]
 
-                    if PIP_VERSION[:2] <= (20, 0):
-                        wheel_cache.cleanup()
-
         return self._dependencies_cache[ireq]
 
     def copy_ireq_dependencies(self, source, dest):
diff --git a/piptools/utils.py b/piptools/utils.py
index b0eca76a6..13c1ae496 100644
--- a/piptools/utils.py
+++ b/piptools/utils.py
@@ -12,7 +12,6 @@
 from pip._internal.vcs import is_url
 from six.moves import shlex_quote
 
-from ._compat import PIP_VERSION
 from .click import style
 
 UNSAFE_PACKAGES = {"setuptools", "distribute", "pip"}
@@ -276,11 +275,7 @@ def get_hashes_from_ireq(ireq):
     in the requirement options.
     """
     result = []
-    if PIP_VERSION[:2] <= (20, 0):
-        ireq_hashes = ireq.options.get("hashes", {})
-    else:
-        ireq_hashes = ireq.hash_options
-    for algorithm, hexdigests in ireq_hashes.items():
+    for algorithm, hexdigests in ireq.hash_options.items():
         for hash_ in hexdigests:
             result.append("{}:{}".format(algorithm, hash_))
     return result
diff --git a/setup.cfg b/setup.cfg
index 7fbaa0efe..50aafcbcc 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -32,7 +32,7 @@ zip_safe = false
 install_requires =
     click >= 7
     six
-    pip >= 20.0
+    pip >= 20.1
 
 [options.packages.find]
 exclude = tests
diff --git a/tests/test_repository_pypi.py b/tests/test_repository_pypi.py
index e072bdd7c..5e9ec117b 100644
--- a/tests/test_repository_pypi.py
+++ b/tests/test_repository_pypi.py
@@ -6,7 +6,6 @@
 from pip._internal.utils.urls import path_to_url
 from pip._vendor.requests import HTTPError, Session
 
-from piptools._compat import PIP_VERSION
 from piptools.repositories import PyPIRepository
 from piptools.repositories.pypi import open_local_or_remote_file
 
@@ -129,20 +128,6 @@ def test_pypirepo_source_dir_is_str(pypi_repository):
     assert isinstance(pypi_repository.source_dir, str)
 
 
-@pytest.mark.skipif(PIP_VERSION[:2] > (20, 0), reason="Refactored in pip==20.1")
-@mock.patch("piptools.repositories.pypi.PyPIRepository.resolve_reqs")  # to run offline
-@mock.patch("piptools.repositories.pypi.WheelCache")
-def test_wheel_cache_cleanup_called(
-    WheelCache, resolve_reqs, pypi_repository, from_line
-):
-    """
-    Test WheelCache.cleanup() called once after dependency resolution.
-    """
-    ireq = from_line("six==1.10.0")
-    pypi_repository.get_dependencies(ireq)
-    WheelCache.return_value.cleanup.assert_called_once_with()
-
-
 def test_relative_path_cache_dir_is_normalized(from_line):
     relative_cache_dir = "pypi-repo-cache"
     pypi_repository = PyPIRepository([], cache_dir=relative_cache_dir)
diff --git a/tox.ini b/tox.ini
index f0439eaf7..da3c82742 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,7 +1,7 @@
 [tox]
 envlist =
     # NOTE: keep this in sync with the env list in .travis.yml for tox-travis.
-    py{27,35,36,37,38,39,py,py3}-pip{20.0,20.1,20.2,latest,master}-coverage
+    py{27,35,36,37,38,39,py,py3}-pip{20.1,20.2,latest,master}-coverage
     checkqa
     readme
 skip_missing_interpreters = True
@@ -12,14 +12,11 @@ extras =
     coverage: coverage
 deps =
     pipmaster: -e git+https://github.com/pypa/pip.git@master#egg=pip
-; TODO: remove all 20.0 mentions after pip-20.2 being released
-    pip20.0: pip==20.0.*
     pip20.1: pip==20.1.*
     pip20.2: pip==20.2.*
 setenv =
     piplatest: PIP=latest
     pipmaster: PIP=master
-    pip20.0: PIP==20.0
     pip20.1: PIP==20.1
     pip20.2: PIP==20.2
 
@@ -45,7 +42,6 @@ commands = twine check {distdir}/*
 
 [travis:env]
 PIP =
-    20.0: pip20.0
     20.1: pip20.1
     20.2: pip20.2
     latest: piplatest