We describe tests of gravitational theory in the strong-field and dynamical regimes. Beginning with binary pulsars, we carry out an arrival-time analysis that reveals the relativistic effects on the time of arrival of radio pulses measured by an observer. We then describe the Hulse-Taylor binary pulsar, the double pulsar, a number of pulsars with white-dwarf companions, and the pulsar in a triple system, and describe the tests of gravitational theories that have been carried out using them. We describe the inspiral of compact binaries in general relativity and scalar-tensor theories, and the tests of gravitational theory that have been carried out using data from the gravitational wave detections of 2015 - 2017. We discuss future tests of general relativity in the strong-field regime, including tests using observations of stars orbiting the black hole at the center of the galaxy, tests involving accretion of matter onto black holes and neutron stars, and cosmological tests.