  Gravitational wave detectors are formidable tools to explore strong-field
gravity, especially black holes and neutron stars. These compact objects are
extraordinarily efficient at producing electromagnetic and gravitational
radiation. As such, they are ideal laboratories for fundamental physics and
have an immense discovery potential. The detection of black hole binaries by
third-generation Earth-based detectors, space-based detectors and pulsar timing
arrays will provide exquisite tests of general relativity. Loud "golden" events
and extreme mass-ratio inspirals can strengthen the observational evidence for
horizons by mapping the exterior spacetime geometry, inform us on possible
near-horizon modifications, and perhaps reveal a breakdown of Einstein's
gravity. Measurements of the black-hole spin distribution and continuous
gravitational-wave searches can turn black holes into efficient detectors of
ultralight bosons across ten or more orders of magnitude in mass. A precise
monitoring of the phase of inspiralling binaries can constrain the existence of
additional propagating fields and characterize the environment in which the
binaries live, bounding the local dark matter density and properties.
Gravitational waves from compact binaries will probe general relativity and
fundamental physics in previously inaccessible regimes, and allow us to address
fundamental issues in our current understanding of the cosmos.
