diff --git a/setup.py b/setup.py
index 977eba5d..084c7707 100644
--- a/setup.py
+++ b/setup.py
@@ -45,21 +45,20 @@ class PyTest(TestCommand):
 
 
 tests_require = [
-    "pytest",
-    "pytest-benchmark",
-    "pytest-cov",
-    "pytest-mock",
-    "pytest-asyncio",
-    "snapshottest",
-    "coveralls",
-    "promise",
-    "six",
-    "mock",
-    "pytz",
-    "iso8601",
+    "pytest>=5.3,<6",
+    "pytest-benchmark>=3.2,<4",
+    "pytest-cov>=2.8,<3",
+    "pytest-mock>=2,<3",
+    "pytest-asyncio>=0.10,<2",
+    "snapshottest>=0.5,<1",
+    "coveralls>=1.11,<2",
+    "promise>=2.3,<3",
+    "mock>=4.0,<5",
+    "pytz==2019.3",
+    "iso8601>=0.1,<2",
 ]
 
-dev_requires = ["black==19.3b0", "flake8==3.7.7"] + tests_require
+dev_requires = ["black==19.10b0", "flake8>=3.7,<4"] + tests_require
 
 setup(
     name="graphene",
@@ -83,9 +82,9 @@ setup(
     keywords="api graphql protocol rest relay graphene",
     packages=find_packages(exclude=["tests", "tests.*", "examples"]),
     install_requires=[
-        "graphql-core>=3.0.3,<4",
-        "graphql-relay>=3.0.0,<4",
-        "aniso8601>=6,<9",
+        "graphql-core>=3.0.3,<3.1",
+        "graphql-relay>=3.0,<4",
+        "aniso8601>=8,<9",
         "unidecode>=1.1.1,<2",
     ],
     tests_require=tests_require,
diff --git a/tox.ini b/tox.ini
index 090cca07..468f5fbc 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = flake8,py36,py37,pre-commit,mypy
+envlist = flake8,py36,py37,py38,pre-commit,mypy
 skipsdist = true
 
 [testenv]
@@ -8,12 +8,12 @@ deps =
 setenv =
      PYTHONPATH = .:{envdir}
 commands =
-    py{36,37}: py.test --cov=graphene graphene examples tests_asyncio {posargs}
+    py{36,37}: pytest --cov=graphene graphene examples tests_asyncio {posargs}
 
 [testenv:pre-commit]
 basepython=python3.7
 deps =
-    pre-commit>0.12.0
+    pre-commit>=2,<3
 setenv =
     LC_CTYPE=en_US.UTF-8
 commands =
@@ -22,12 +22,12 @@ commands =
 [testenv:mypy]
 basepython=python3.7
 deps =
-    mypy>=0.720
+    mypy>=0.761,<1
 commands =
     mypy graphene
 
 [testenv:flake8]
-basepython=python3.6
+basepython=python3.7
 deps =
     flake8>=3.7,<4
 commands =