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The observation of the inspiral and merger of compact binaries by theLIGO/Virgo collaboration ushered in a new era in the study of strong-fieldgravity. We review current and future tests of strong gravity and of the Kerrparadigm with gravitational-wave interferometers, both within a theory-agnosticframework (the parametrized post-Einsteinian formalism) and in the context ofspecific modified theories of gravity (scalar-tensor,Einstein-dilaton-Gauss-Bonnet, dynamical Chern-Simons, Lorentz-violating, andextra dimensional theories). In this contribution we focus on (i) theinformation carried by the inspiral radiation, and (ii) recent progress innumerical simulations of compact binary mergers in modified gravity.

Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (I) Inspiral-Merger