  Coalescence of binary supermassive black holes (SBHs) would constitute the
strongest sources of gravitational waves to be observed by LISA. While the
formation of binary SBHs during galaxy mergers is almost inevitable,
coalescence requires that the separation between binary components first drop
by a few orders of magnitude, due presumably to interaction of the binary with
stars and gas in a galactic nucleus. This article reviews the observational
evidence for binary SBHs and discusses how they would evolve. No completely
convincing case of a bound, binary SBH has yet been found, although a handful
of systems (e.g. interacting galaxies; remnants of galaxy mergers) are now
believed to contain two SBHs at projected separations of roughly one kpc.
N-body studies of binary evolution in gas-free galaxies have reached large
enough particle numbers to reproduce the slow, "diffusive" refilling of the
binary's loss cone that is believed to characterize binary evolution in real
galactic nuclei. While some of the results of these simulations -- e.g. the
binary hardening rate and eccentricity evolution -- are strongly $N$-dependent,
others -- e.g. the "damage" inflicted by the binary on the nucleus -- are not.
Luminous early-type galaxies often exhibit depleted cores with masses of 1-2
times the mass of their nuclear SBHs, consistent with the predictions of the
binary model. Studies of the interaction of massive binaries with gas are still
in their infancy, although much progress is expected in the near future. Binary
coalescence has a large influence on the spins of SBHs, even for mass ratios as
extreme as 10:1, and evidence of spin-flips may have been observed.
