Despite solid theoretical and observational grounds for the pairing of
supermassive black holes (SMBHs) after galaxy mergers, definitive evidence for
the existence of close (sub-parsec) separation SMBH binaries (SMBHBs)
approaching merger is yet to be found. This chapter reviews techniques aimed at
discovering such SMBHBs in galactic nuclei. We motivate the search with a brief
overview of SMBHB formation and evolution, and the gaps in our present-day
theoretical understanding. We then present existing observational evidence for
SMBHBs and discuss ongoing efforts to provide definitive evidence for a
population at sub-parsec orbital separations, where many of the aforementioned
theoretical gaps lie. We conclude with future prospects for discovery with
electromagnetic (primarily time-domain) surveys, high-resolution imaging
experiments, and low-frequency gravitational-wave detectors.Comment: To appear in Chapter 5 in the book Black Holes in the Era of
Gravitational Wave Astronomy, ed. Arca Sedda, Bortolas, Spera, pub. Elsevier.
All authors equally contributed to the Chapter writin