  The recent LIGO detection of gravitational waves from black-hole binaries
offers the exciting possibility of testing gravitational theories in the
previously inaccessible strong-field, highly relativistic regime. While the
LIGO detections are so far consistent with the predictions of General
Relativity, future gravitational-wave observations will allow us to explore
this regime to unprecedented accuracy. One of the generic predictions of
theories of gravity that extend General Relativity is the violation of the
strong equivalence principle, i.e. strongly gravitating bodies such as neutron
stars and black holes follow trajectories that depend on their nature and
composition. This has deep consequences for gravitational-wave emission, which
takes place with additional degrees of freedom besides the tensor polarizations
of General Relativity. I will briefly review the formalism needed to describe
these extra emission channels, and show that binary black-hole observations
probe a set of gravitational theories that are largely disjoint from those that
are testable with binary pulsars or neutron stars.
