The capture and disruption of stars by supermassive black holes (SMBHs), and the formation and coalescence of binaries, are inevitable consequences of the presence of SMBHs at the cores of galaxies. Pairs of active galactic nuclei (AGN) and binary SMBHs are important stages in the evolution of galaxy mergers, and an intense search for these systems is currently ongoing. In the early and advanced stages of galaxy merging, observations of the triggering of accretion onto one or both BHs inform us about feedback processes and BH growth. Identification of the compact binary SMBHs at parsec and sub-parsec scales provides us with important constraints on the interaction processes that govern the shrinkage of the binary beyond the “final parsec”. Coalescing binary SMBHs are among the most powerful sources of gravitational waves (GWs) in the universe. Stellar tidal disruption events (TDEs) appear as luminous, transient, accretion flares when part of the stellar material is accreted by the SMBH. About 30 events have been identified by multi-wavelength observations by now, and they will be detected in the thousands in future ground-based or space-based transient surveys. The study of TDEs provides us with a variety of new astrophysical tools and applications, related to fundamental physics or astrophysics. Here, we provide a review of the current status of observations of SMBH pairs and binaries, and TDEs, and discuss astrophysical implications.