diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index b275f07d..1e9dff20 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -16,12 +16,12 @@ jobs:
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        python-version: ["3.7", "3.8", "3.9"]
+        python-version: ["3.7", "3.8", "3.9", "3.10"]
         os: ["ubuntu-latest"]
         include:
-          - python-version: "3.8"
+          - python-version: "3.9"
             os: "macos-latest"
-          - python-version: "3.8"
+          - python-version: "3.9"
             os: "windows-latest"
 
     steps:
diff --git a/.gitignore b/.gitignore
index a92a8e56..b4f553f2 100644
--- a/.gitignore
+++ b/.gitignore
@@ -22,3 +22,4 @@ emcee_version.py
 .tox
 env
 .eggs
+.coverage.*
diff --git a/docs/conf.py b/docs/conf.py
index 742d2ea2..b52d97fc 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -48,5 +48,5 @@
     "use_repository_button": True,
     "use_download_button": True,
 }
-jupyter_execute_notebooks = "off"
-execution_timeout = -1
+nb_execution_mode = "off"
+nb_execution_timeout = -1
diff --git a/src/emcee/state.py b/src/emcee/state.py
index e6555f3c..9d3413f6 100644
--- a/src/emcee/state.py
+++ b/src/emcee/state.py
@@ -44,6 +44,11 @@ def __init__(
         self.blobs = dc(blobs)
         self.random_state = dc(random_state)
 
+    def __len__(self):
+        if self.blobs is None:
+            return 3
+        return 4
+
     def __repr__(self):
         return "State({0}, log_prob={1}, blobs={2}, random_state={3})".format(
             self.coords, self.log_prob, self.blobs, self.random_state
@@ -55,3 +60,16 @@ def __iter__(self):
         return iter(
             (self.coords, self.log_prob, self.random_state, self.blobs)
         )
+
+    def __getitem__(self, index):
+        if index < 0:
+            return self[len(self) + index]
+        if index == 0:
+            return self.coords
+        elif index == 1:
+            return self.log_prob
+        elif index == 2:
+            return self.random_state
+        elif index == 3 and self.blobs is not None:
+            return self.blobs
+        raise IndexError("Invalid index '{0}'".format(index))
diff --git a/src/emcee/tests/unit/test_state.py b/src/emcee/tests/unit/test_state.py
index 9ecaa838..0150eb46 100644
--- a/src/emcee/tests/unit/test_state.py
+++ b/src/emcee/tests/unit/test_state.py
@@ -1,11 +1,16 @@
 # -*- coding: utf-8 -*-
 
 import numpy as np
+import pytest
 
 from emcee import EnsembleSampler
 from emcee.state import State
 
 
+def check_rstate(a, b):
+    assert all(np.allclose(a_, b_) for a_, b_ in zip(a[1:], b[1:]))
+
+
 def test_back_compat(seed=1234):
     np.random.seed(seed)
     coords = np.random.randn(16, 3)
@@ -18,13 +23,13 @@ def test_back_compat(seed=1234):
     assert np.allclose(coords, c)
     assert np.allclose(log_prob, l)
     assert np.allclose(blobs, b)
-    assert all(np.allclose(a, b) for a, b in zip(rstate[1:], r[1:]))
+    check_rstate(rstate, r)
 
     state = State(coords, log_prob, None, rstate)
     c, l, r = state
     assert np.allclose(coords, c)
     assert np.allclose(log_prob, l)
-    assert all(np.allclose(a, b) for a, b in zip(rstate[1:], r[1:]))
+    check_rstate(rstate, r)
 
 
 def test_overwrite(seed=1234):
@@ -40,3 +45,28 @@ def ll(x):
     sampler = EnsembleSampler(nwalkers, 1, ll)
     sampler.run_mcmc(p0, 10)
     assert np.allclose(init, p0)
+
+
+def test_indexing(seed=1234):
+    np.random.seed(seed)
+    coords = np.random.randn(16, 3)
+    log_prob = np.random.randn(len(coords))
+    blobs = np.random.randn(len(coords))
+    rstate = np.random.get_state()
+
+    state = State(coords, log_prob, blobs, rstate)
+    np.testing.assert_allclose(state[0], state.coords)
+    np.testing.assert_allclose(state[1], state.log_prob)
+    check_rstate(state[2], state.random_state)
+    np.testing.assert_allclose(state[3], state.blobs)
+    np.testing.assert_allclose(state[-1], state.blobs)
+    with pytest.raises(IndexError):
+        state[4]
+
+    state = State(coords, log_prob, random_state=rstate)
+    np.testing.assert_allclose(state[0], state.coords)
+    np.testing.assert_allclose(state[1], state.log_prob)
+    check_rstate(state[2], state.random_state)
+    check_rstate(state[-1], state.random_state)
+    with pytest.raises(IndexError):
+        state[3]
diff --git a/tox.ini b/tox.ini
index 68e259a2..d759fa63 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,11 +1,12 @@
 [tox]
-envlist = py{37,38,39}{,-extras},lint
+envlist = py{37,38,39,310}{,-extras},lint
 
 [gh-actions]
 python =
     3.7: py37
     3.8: py38
     3.9: py39-extras
+    3.10: py310
 
 [testenv]
 deps = coverage[toml]