diff --git a/spec/verification_test_suite.md b/spec/verification_test_suite.md
index ece853e4f..cbe770e48 100644
--- a/spec/verification_test_suite.md
+++ b/spec/verification_test_suite.md
@@ -1,8 +1,62 @@
 # Verification - test suite
 
+## Measuring conformance
 
+In addition to the specification documents, a test suite is being developed to
+aid library developers check conformance to the spec. **NOTE: The test suite
+is still a work in progress.** It can be found at
+<https://github.com/data-apis/array-api-tests>.
 
-## Measuring conformance
+It is important to note that while the aim of the array API test suite is to
+cover as much of the spec as possible, there are necessarily some aspects of
+the spec that are not covered by the test suite, typically because they are
+impossible to effectively test. Furthermore, if the test suite appears to
+diverge in any way from what the spec documents say, this should be considered
+a bug in the test suite. The specification is the ground source of truth.
+
+## Running the tests
+
+To run the tests, first clone the [test suite
+repo](https://github.com/data-apis/array-api-tests), and install the testing
+dependencies,
+
+    pip install pytest hypothesis
+
+or
+
+    conda install pytest hypothesis
+
+as well as the array libraries that you want to test. To run the tests, you
+need to specify the array library that is to be tested. There are two ways to
+do this. One way is to set the `ARRAY_API_TESTS_MODULE` environment variable.
+For example
+
+    ARRAY_API_TESTS_MODULE=numpy pytest
+
+Alternatively, edit the `array_api_tests/_array_module.py` file and change the
+line
+
+```py
+array_module = None
+```
+
+to
+
+```py
+import numpy as array_module
+```
+
+(replacing `numpy` with the array module namespace to be tested).
+
+In either case, the tests should be run with the `pytest` command.
+
+Aside from the two testing dependencies (`pytest` and `hypothesis`), the test
+suite has no dependencies. In particular, it does not depend on any specific
+array libraries such as NumPy. All tests are run using only the array library
+that is being tested, comparing results against the behavior as defined in the
+spec. The test suite is designed to be standalone so that it can easily be vendored.
 
-TODO: explain how to use the test suite to measure and report on the level of
-(non-)conformance.
+See the
+[README](https://github.com/data-apis/array-api-tests/blob/master/README.md)
+in the test suite repo for more information about how to run and interpret the
+test suite results.