diff --git a/.github/workflows/push-test.yml b/.github/workflows/push-test.yml
index 46696b7..9c1e03a 100644
--- a/.github/workflows/push-test.yml
+++ b/.github/workflows/push-test.yml
@@ -57,4 +57,68 @@ jobs:
       # https://github.com/marketplace/actions/install-poetry-action#codecov-upload
       # ======
       - name: Run tests
-        run: poetry run pytest
\ No newline at end of file
+        run: poetry run pytest
+
+  benchmarks:
+    name: ASV Benchmarks
+    needs: test
+    runs-on: ubuntu-22.04
+    strategy:
+      matrix:
+        python-version: ["3.9"]
+        poetry-version: ["1.2.1"]
+    steps:
+      # ======
+      # Checkout, set up python
+      # ======
+      - name: Check out
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v4
+        with:
+          python-version: ${{ matrix.python-version }}
+      # ======
+      # Install and configure poetry
+      # ======
+      - name: Load cached Poetry installation
+        id: cached-poetry
+        uses: actions/cache@v4
+        with:
+          path: ~/.local  # the path depends on the OS
+          key: poetry-${{ matrix.poetry-version }}
+      - name: Install Poetry
+        if: steps.cached-poetry.outputs.cache-hit != 'true'
+        uses: snok/install-poetry@v1
+        with:
+          version: ${{ matrix.poetry-version }}
+          virtualenvs-create: true
+          virtualenvs-in-project: true
+      # ======
+      # Load cached venv if cache exists
+      # Install dependencies if cache does not exist
+      # ======
+      - name: Load cached venv
+        id: cached-poetry-dependencies-dev
+        uses: actions/cache@v4
+        with:
+          path: .venv
+          key: dev-${{ matrix.python-version }}-${{ matrix.poetry-version }}-${{ hashFiles('**/poetry.lock') }}
+      - name: Install dependencies
+        if: steps.cached-poetry-dependencies-dev.outputs.cache-hit != 'true'
+        run: poetry install --no-interaction -E dev
+      # ======
+      # Compare benchmarks between master and PR, and fail if any get worse
+      # ======
+
+      - name: Setup ASV
+        run: |
+          pip install asv
+          cd asv_bench
+          asv machine --yes
+      - name: Check regression
+        run: |
+          cd asv_bench
+          git fetch origin $GITHUB_BASE_REF:base $GITHUB_REF:pr
+          asv continuous base pr -e
diff --git a/.gitignore b/.gitignore
index 21ef3e1..c362d7c 100644
--- a/.gitignore
+++ b/.gitignore
@@ -120,3 +120,11 @@ venv.bak/
 
 # Exploratory work
 playground/
+
+# Unit / Performance Testing #
+##############################
+asv_bench/.asv/env/
+asv_bench/.asv/html/
+asv_bench/.asv/results/
+asv_bench/derivative/
+test-data.xml
diff --git a/asv_bench/asv.conf.json b/asv_bench/asv.conf.json
new file mode 100644
index 0000000..fcf0ca6
--- /dev/null
+++ b/asv_bench/asv.conf.json
@@ -0,0 +1,14 @@
+{
+    "version": 1,
+    "project": "derivative",
+    "project_url": "https://derivative.readthedocs.io/",
+    "repo": "..",
+    "environment_type": "virtualenv",
+    "env_dir": ".asv/env",
+    "results_dir": ".asv/results",
+    "html_dir": ".asv/html",
+    "show_commit_url": "https://github.com/$OWNER/$REPO/commit/",
+    "build_command": [
+        "python -m build --outdir {build_cache_dir} {build_dir}"
+    ]
+}
diff --git a/asv_bench/benchmarks/__init__.py b/asv_bench/benchmarks/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/asv_bench/benchmarks/finite_difference_1D.py b/asv_bench/benchmarks/finite_difference_1D.py
new file mode 100644
index 0000000..d31149a
--- /dev/null
+++ b/asv_bench/benchmarks/finite_difference_1D.py
@@ -0,0 +1,19 @@
+# Write the benchmarking functions here.
+# See "Writing benchmarks" in the asv docs for more information.
+import numpy as np
+from derivative import FiniteDifference
+
+class FiniteDifferenceBM:
+    """
+    An example benchmark that times the performance of various kinds
+    of iterating over dictionaries in Python.
+    """
+    def setup(self):
+        self.differentiator = FiniteDifference(k=1)
+        self.t = np.arange(0, 2 * np.pi, .01)
+
+    def time_derivative(self):
+        self.differentiator.d(X=self.t, t=self.t, axis=0)
+
+    def peakmem_derivative(self):
+        self.differentiator.d(X=self.t, t=self.t, axis=0)
diff --git a/pyproject.toml b/pyproject.toml
index e582424..0876f2f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -30,11 +30,12 @@ matplotlib = {version = "^3.2.1", optional = true}
 #pandoc = {version = "^2.2", optional = true}
 
 # dev
+asv = {version = "^0.6", optional = true}
 pytest = {version = "^7", optional = true}
 
 [tool.poetry.extras]
 docs = ["sphinx", "nbsphinx", "ipykernel", "jupyter_client", "matplotlib", "pandoc"]
-dev = ["pytest"]
+dev = ["asv", "pytest"]
 
 [build-system]
 requires = ["poetry-core>=1.1.0"]