Supermassive black hole binaries (SMBHBs) are expected due to galaxy mergers and the ubiquity of central supermassive black holes (SMBHs) in galaxies, but direct evidence for close-separation SMBHBs has been elusive. This thesis presents my search for SMBHBs in the optical time domain, {\it i.e.} by searching for their optical variability signatures. It is a novel approach that can potentially yield SMBHBs in close, sub-pc orbits, a population of SMBH pairs or binaries that can not be directly imaged or resolved by current telescopes or techniques. Further, searches in the optical time domain are sensitive to SMBHBs in the low-frequency gravitational wave-emitting regime, opening up the possibility of studying them in the era of multi-messenger astronomy.

I developed a custom pipeline to systematically search in the Pan-STARRS1 Medium Deep Survey (PS1 MDS) for periodically varying quasars, which have been predicted as the manifestations of SMBHBs at close separations. I constructed a spectroscopically-complete sample of SMBHB candidates using observations with the Gemini Telescope or the Discovery Channel Telescope and measured their black hole masses and redshifts. I also followed up the candidates with a dedicated monitoring program on the Las Cumbres Observatory telescopes, in order to put their periodicity to the test and identify false positives that are due to the stochastic variability of regular quasars that do not host SMBHBs. I set up the expectations for a true periodic signal by modeling normal quasar variability and showed that evidence for a true signal should strengthen over a longer temporal baseline. I then used the expectations as a guide and applied a range of statistical criteria to select more robust candidates from PS1 MDS. From this down-selected sample, I was able to determine an upper limit on the SMBHB rate. I also discussed the search for SMBHBs in the era of the Large Synoptic Survey Telescope and SMBHB candidates as possible gravitational wave sources for the pulsar timing arrays.