Pulsars are spinning neutron stars typically observed as pulses emitted at radio wavelengths. These pulsations exhibit a rotational stability that rival the best atomic clocks, making pulsars one of the most important tools for resolving gravitational phenomena in extreme environments. I will present an overview of the ways in which radio pulsars can be used to test strong-field gravity and observe gravitational radiation, both in the context of historical and ongoing experiments. I will also describe how these measurements can be translated to sought-after quantities like the masses and moments of inertia of neutron stars.