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