Strong-field tests of gravity with gravitational waves

Recent observations of black holes and neutron stars through gravitational waves allow us to probe the strong and dynamical field regime of gravity. There are two main ways to test gravity, (i) model-independent and (ii) theory-specific. After reviewing the current observational status, I will first describe a theory-agnostic way of testing General Relativity with gravitational waves by parameterizing the waveforms. I will next explain a theory-specific test, in particular focusing on testing a theory with higher curvature corrections in the action motivated by string theory. I will describe how one can derive the current strongest bound on the theory from gravitational-wave observations.