diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index d4d20dd6..565a68ce 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -7,7 +7,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [ 3.5, 3.6, 3.7, 3.8, 3.9, ]
+        python-version: [ 3.6, 3.7, 3.8, 3.9, ]
     steps:
       - uses: actions/checkout@v2
 
@@ -26,24 +26,3 @@ jobs:
 
       - name: Codecov upload
         run: codecov
-
-  # tox-gh-actions requires Python >= 3.5, so test 3.4 separately
-  test-py34:
-    runs-on: ubuntu-18.04
-    steps:
-      - uses: actions/checkout@v2
-
-      - name: Setup Python 3.4
-        uses: actions/setup-python@v2
-        with:
-          python-version: 3.4
-
-      - name: Install dependencies
-        run: |
-          pip install tox codecov
-
-      - name: Run tests
-        run: tox -e py34
-
-      - name: Codecov upload
-        run: codecov
diff --git a/appveyor.yml b/appveyor.yml
index 4a334429..08ef1a6c 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -2,7 +2,7 @@ environment:
   matrix:
     - TOXENV: "py37"
       TOX_APPVEYOR_X64: "1"
-    - TOXENV: "py35"
+    - TOXENV: "py36"
       TOX_APPVEYOR_X64: "0"
 
 # The Python version here doesn't matter (except that the commands have the same),
diff --git a/doc/pyproject_toml.rst b/doc/pyproject_toml.rst
index 304f847b..8b144cfc 100644
--- a/doc/pyproject_toml.rst
+++ b/doc/pyproject_toml.rst
@@ -30,6 +30,10 @@ Version constraints:
 - :ref:`pyproject_toml_project` requires ``flit_core >=3.2``
 - :ref:`pyproject_old_metadata` requires ``flit_core >=2,<4``
 - The older :doc:`flit.ini file <flit_ini>` requires ``flit_core <3``.
+- TOML features new in version 1.0 require ``flit_core >=3.4``.
+- ``flit_core`` 3.3 is the last version supporting Python 3.4 & 3.5. Packages
+  supporting these Python versions can only use `TOML v0.5
+  <https://toml.io/en/v0.5.0>`_.
 - Only ``flit_core`` 2.x can build packages on Python 2, so packages still
   supporting Python 2 cannot use new-style metadata (the ``[project]`` table).
 
@@ -333,10 +337,10 @@ Here's the full metadata section from flit itself:
         "flit_core>=2.2.0",
         "requests",
         "docutils",
-        "toml",
-        "zipfile36; python_version in '3.3 3.4 3.5'",
+        "tomli",
+        "tomli-w",
     ]
-    requires-python=">=3.5"
+    requires-python=">=3.6"
     description-file="README.rst"
     classifiers=[
         "Intended Audience :: Developers",
diff --git a/flit/init.py b/flit/init.py
index 496166c4..f2f5d407 100644
--- a/flit/init.py
+++ b/flit/init.py
@@ -4,7 +4,7 @@
 from pathlib import Path
 import re
 import sys
-import toml
+import tomli_w
 
 def get_data_dir():
     """Get the directory path for flit user data files.
@@ -223,13 +223,14 @@ def initialise(self):
                 name=json.dumps(module), authors=authors_list
             ))
             if readme:
-                toml.dump({'readme': readme}, f)
+                f.write(tomli_w.dumps({'readme': readme}))
             if classifiers:
                 f.write(f"classifiers = {json.dumps(classifiers)}\n")
             f.write('dynamic = ["version", "description"]\n')
             if home_page:
-                f.write("\n")
-                toml.dump({'project': {'urls': {'Home': home_page}}}, f)
+                f.write("\n" + tomli_w.dumps({
+                    'project': {'urls': {'Home': home_page}}
+                }))
 
         print()
         print("Written pyproject.toml; edit that file to add optional extra info.")
diff --git a/flit/tomlify.py b/flit/tomlify.py
index d50cc9ee..e4796cd2 100644
--- a/flit/tomlify.py
+++ b/flit/tomlify.py
@@ -5,7 +5,7 @@
 import configparser
 import os
 from pathlib import Path
-import toml
+import tomli_w
 
 from .config import metadata_list_fields
 
@@ -49,11 +49,11 @@ def convert(path):
 
     written_entrypoints = False
     with Path('pyproject.toml').open('w', encoding='utf-8') as f:
-        f.write(TEMPLATE.format(metadata=toml.dumps(metadata)))
+        f.write(TEMPLATE.format(metadata=tomli_w.dumps(metadata)))
 
         if scripts:
             f.write('\n[tool.flit.scripts]\n')
-            toml.dump(scripts, f)
+            f.write(tomli_w.dumps(scripts))
 
         for groupname, group in entrypoints.items():
             if not dict(group):
@@ -62,7 +62,7 @@ def convert(path):
             if '.' in groupname:
                 groupname = '"{}"'.format(groupname)
             f.write('\n[tool.flit.entrypoints.{}]\n'.format(groupname))
-            toml.dump(OrderedDict(group), f)
+            f.write(tomli_w.dumps(OrderedDict(group)))
             written_entrypoints = True
 
     print("Written 'pyproject.toml'")
diff --git a/flit_core/flit_core/build_thyself.py b/flit_core/flit_core/build_thyself.py
index f3aaf7cb..7f6edea3 100644
--- a/flit_core/flit_core/build_thyself.py
+++ b/flit_core/flit_core/build_thyself.py
@@ -25,9 +25,9 @@
     'summary': ('Distribution-building parts of Flit. '
                     'See flit package for more information'),
     'requires_dist': [
-        'toml',
+        'tomli',
     ],
-    'requires_python': '>=3.4',
+    'requires_python': '>=3.6',
     'classifiers': [
         "License :: OSI Approved :: BSD License",
         "Topic :: Software Development :: Libraries :: Python Modules",
diff --git a/flit_core/flit_core/config.py b/flit_core/flit_core/config.py
index 84c1ecc2..53a4f856 100644
--- a/flit_core/flit_core/config.py
+++ b/flit_core/flit_core/config.py
@@ -5,7 +5,7 @@
 import os
 import os.path as osp
 from pathlib import Path
-import toml
+import tomli
 import re
 
 from .versionno import normalise_version
@@ -66,8 +66,7 @@ class ConfigError(ValueError):
 def read_flit_config(path):
     """Read and check the `pyproject.toml` file with data about the package.
     """
-    with path.open('r', encoding='utf-8') as f:
-        d = toml.load(f)
+    d = tomli.loads(path.read_text('utf-8'))
     return prep_toml_config(d, path)
 
 
diff --git a/pyproject.toml b/pyproject.toml
index f89fab7d..7a613581 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,8 +11,8 @@ dependencies = [
     "flit_core >=3.3.0",
     "requests",
     "docutils",
-    "toml",
-    "zipfile36; python_version == '3.5'",
+    "tomli",
+    "tomli-w",
 ]
 requires-python = ">=3.6"
 readme = "README.rst"
diff --git a/tests/test_init.py b/tests/test_init.py
index c30e6d36..26a974b0 100644
--- a/tests/test_init.py
+++ b/tests/test_init.py
@@ -6,7 +6,7 @@
 from unittest.mock import patch
 import pytest
 
-import toml
+import tomli
 
 from flit import init
 
@@ -106,8 +106,8 @@ def test_init():
 
         generated = Path(td) / 'pyproject.toml'
         assert_isfile(generated)
-        with generated.open() as f:
-            data = toml.load(f)
+        with generated.open('rb') as f:
+            data = tomli.load(f)
         assert data['project']['authors'][0]['email'] == "test@example.com"
         license = Path(td) / 'LICENSE'
         assert_isfile(license)
@@ -129,8 +129,8 @@ def test_init_homepage_and_license_are_optional():
           faking_input(responses):
         ti = init.TerminalIniter(td)
         ti.initialise()
-        with Path(td, 'pyproject.toml').open() as f:
-            data = toml.load(f)
+        with Path(td, 'pyproject.toml').open('rb') as f:
+            data = tomli.load(f)
         assert not Path(td, 'LICENSE').exists()
     assert data['project'] == {
         'authors': [{'name': 'Test Author', 'email': 'test_email@example.com'}],
@@ -151,8 +151,8 @@ def test_init_homepage_validator():
           faking_input(responses):
         ti = init.TerminalIniter(td)
         ti.initialise()
-        with Path(td, 'pyproject.toml').open() as f:
-            data = toml.load(f)
+        with Path(td, 'pyproject.toml').open('rb') as f:
+            data = tomli.load(f)
     assert data['project'] == {
         'authors': [{'name': 'Test Author', 'email': 'test_email@example.com'}],
         'name': 'test_module_name',
@@ -172,8 +172,8 @@ def test_author_email_field_is_optional():
           faking_input(responses):
         ti = init.TerminalIniter(td)
         ti.initialise()
-        with Path(td, 'pyproject.toml').open() as f:
-            data = toml.load(f)
+        with Path(td, 'pyproject.toml').open('rb') as f:
+            data = tomli.load(f)
         assert not Path(td, 'LICENSE').exists()
 
     assert data['project'] == {
@@ -213,8 +213,8 @@ def test_init_readme_found_yes_choosen():
           faking_input(responses):
         ti = init.TerminalIniter(td)
         ti.initialise()
-        with Path(td, 'pyproject.toml').open() as f:
-            data = toml.load(f)
+        with Path(td, 'pyproject.toml').open('rb') as f:
+            data = tomli.load(f)
 
     assert data['project'] == {
         'authors': [{'name': 'Test Author', 'email': 'test_email@example.com'}],
diff --git a/tests/test_tomlify.py b/tests/test_tomlify.py
index a7b79785..d6a35c45 100644
--- a/tests/test_tomlify.py
+++ b/tests/test_tomlify.py
@@ -1,6 +1,6 @@
 import os
 from pathlib import Path
-import toml
+import tomli
 from shutil import copy
 from testpath import assert_isfile
 
@@ -17,8 +17,8 @@ def test_tomlify(copy_sample, monkeypatch):
     pyproject_toml = (td / 'pyproject.toml')
     assert_isfile(pyproject_toml)
 
-    with pyproject_toml.open(encoding='utf-8') as f:
-        content = toml.load(f)
+    with pyproject_toml.open('rb') as f:
+        content = tomli.load(f)
 
     assert 'build-system' in content
     assert 'tool' in content
diff --git a/tox.ini b/tox.ini
index 1ca9e387..59ddc05d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,11 +1,9 @@
 [tox]
-envlist = py{39,38,37,36,35,34},bootstrap
+envlist = py{39,38,37,36},bootstrap
 skip_missing_interpreters = true
 
 [gh-actions]
 python =
-    3.4: py34
-    3.5: py35
     3.6: py36
     3.7: py37
     3.8: py38, bootstrap
@@ -18,16 +16,11 @@ deps =
     testpath
     responses
     docutils
-    toml
+    tomli
+    tomli-w
     pytest>=2.7.3
     pytest-cov
 
-    py35: zipfile36
-    py34: zipfile36
-
-    # pytest requires attrs, and it now gets a version for Py >= 3.5 by default
-    py34: attrs <21
-
 skip_install=true
 
 setenv =
@@ -36,15 +29,6 @@ setenv =
 commands =
     python -m pytest --cov=flit --cov=flit_core/flit_core
 
-# Python 3.4 & 3.5: only test flit_core
-[testenv:py34]
-commands =
-    python -m pytest --cov=flit_core/flit_core --pyargs flit_core
-
-[testenv:py35]
-commands =
-    python -m pytest --cov=flit_core/flit_core --pyargs flit_core
-
 [testenv:bootstrap]
 skip_install = true
 # Make the install step a no-op, so nothing gets installed in the env