The Electromagnetic Counterparts of Supermassive Black Hole Binaries The gravitational waves emitted by supermassive black hole binaries at cosmological distances are expected to be detectable by the future Laser Interferometric Space Antenna (LISA). While the gravitational waves themselves will provide a treasure trove of information, if the source can be identified in electromagnetic bands, this would open up entirely new scientific opportunities, to probe black hole astrophysics, cosmology, and novel aspects of gravitational physics. Any detectable emission from these supermassive black hole binaries is likely to be time-variable, and I will argue that this may make the identification feasible. Possibilities for such variable emission include a roughly periodic signal due to the orbital motion prior to coalescence, a transient precursor, caused by the gas trapped inside the binary's orbit, and a transient "after-glow" produced by merger-induced shocks in the circumbinary disk and by post-merger gas accretion. I will discuss how these time-variable signatures may be detectable, and how they can help in identifying a unique counterpart, even with the relatively poor (fraction of a square degree) sky localization provided by LISA.