Theory-specific and theory-agnostic tests of gravity with gravitational wave data

The third observing run of the advanced ground-based detector network has yielded dozens of detections of gravitational waves from merging black holes and neutron stars. These detections have offered new insights into the physics and astrophysics of black holes and the nature of gravity. In this talk I will discuss recent results regarding theory-specific and theory-agnostic tests of gravity, prospects for the next observing run, as well as challenges and the role of analysis systematics as the number of detections and the network sensitivity increases.