  Extreme-mass-ratio inspirals consist of binary systems of compact objects,
with orders of magnitude differences in their masses, in the regime where the
dynamics are driven by gravitational wave emission. The unique nature of
extreme-mass-ratio inspirals facilitates the exploration of diverse and
stimulating tests related to various aspects of black holes and General
Relativity. These tests encompass investigations into the spacetime geometry,
the dissipation of the binary system energy and angular momentum, and the
impact of the intrinsic non-linear effects of the gravitational interaction.
This review accounts for the manifold opportunities for testing General
Relativity, ranging from examinations of black hole properties to cosmological
and multimessenger tests.
