Binary black holes occupy a special place in our quest for understanding the evolution of galaxies along cosmic history. If massive black holes grow at the center of (pre-)galactic structures that experience a sequence of merger episodes, then binary black holes form as inescapable outcome of galaxy assembly, and can in principle be detected as powerful dual or binary quasars. But, if the black holes reach coalescence, during their inspiral inside the galaxy remnant, then they become the loudest sources of gravitational waves ever in the universe that the Laser Interferometer Space Antenna will reveal out to very look back times. Through galaxy mergers Nature provides the pathway for the formation of these binaries, and a number of key questions rise: How do massive black holes pair in a merger? Depending on the structure of the underlying galaxies, do black holes always form a close Keplerian binary in its pathway to coalescence? What is the role played by gas and/or stars in braking the black holes, and on which timescale does coalescence occur? Can the black holes accrete during their inspiral and re-orient their spins prior to coalescence? Can we associate an AGN activity to the different dynamical phases? After reviewing the progress made in understanding/tracing the black hole dynamics in gas-rich mergers, we describe the current status of the observational search on dual/binary/recoiling AGN and discuss future perspectives.