The study of galaxy mergers and supermassive binary black holes (SMBBHs) is central to our understanding of the galaxy and black hole assembly and (co-)evolution at the epoch of structure formation and throughout cosmic history. Galaxy mergers are the sites of major accretion episodes, they power quasars, grow supermassive black holes (SMBHs), and drive SMBH-host scaling relations. The coalescing SMBBHs at their centers are the loudest sources of gravitational waves (GWs) in the universe, and the subsequent GW recoil has a variety of potential astrophysical implications which are still under exploration. Future GW astronomy will open a completely new window on structure formation and galaxy mergers, including the direct detection of coalescing SMBBHs, high-precision measurements of their masses and spins, and constraints on BH formation and evolution in the high-redshift universe.