Evidence for Supermassive Black Holes at the centers of galaxy bulges, combined with the paradigm of hierarchical structure formation, implies the existence of binary Supermassive Black Holes. It is expected that these binaries themselves will eventually coalesce in what would be the brightest gravitational-radiation events in the astrophysical universe. In this talk, we discuss the effect of the overall galaxy merger rate as well as dynamical processes at the centers of galaxies that might effect this scenario, in particular the so-called “final parsec problem” indicating that a significant fraction of the binaries may stall before they can coalesce. I discuss the theoretical prospects for resolving this problem, and the observational prospects for observing the gravitational radiation, both as a stochastic background of objects in the quiescent quasi-Newtonian phase and via the bright final coalescence of individual binaries using instruments such as LISA.