  The formation and growth of black holes can strongly influence the
distribution of dark matter around them. I discuss here the different types of
dark matter overdensities around black holes, including dark matter cusps,
spikes, mounds, crests, and gravitational atoms. I then review recent results
on the evolution of a black holes binary in presence of dark matter, focusing
on the energy transfer between binary and dark matter induced by dynamical
friction. Finally, I present the prospects for studying dark matter with
gravitational wave observations, and argue that future interferometers might be
able to detect and characterise dark matter overdensities around black holes.
