The observed structure of the universe suggests that galaxy mergers and the co-evolution of their central supermassive black holes (SMBHs) are common throughout the cosmos. While the formation of binary SMBHs seems inevitable, direct observational evidence of binary SMBHs has been elusive. The evolution of binary SMBHs from kilo-parsec to subparsec and their interactions with host galaxies are still poorly understood. Active SMBHs, known as quasars, provide an excellent way to study distant SMBHs in electromagnetic waves. My thesis consists of several studies aimed at searching for dual and binary quasars on different scales, from kilo-parsec to milli-parsec. At kilo-parsec scales, large systematic searches at cosmic noon are limited by the stringent angular resolution requirement of ground-based optical surveys. I will present a novel astrometric technique, called Varstrometry, to search for unresolved dual quasars using all-sky surveys like Gaia. The follow-up Hubble Space Telescope observations reveal dozens of kpc dual quasar candidates. Using multi-wavelength observations, I will also report a confirmed kpc dual quasar in a galaxy merger at cosmic noon. At smaller scales of (sub-)parsec, two SMBHs are so close that direct imaging is not plausible. I will show the periodic quasar candidates found from ~20-yr optical light curves made by combining the Sloan Digital Sky Survey and the Dark Energy Survey. The periodic quasar candidates are potential binary SMBHs at sub-pc scales. Finally, I will discuss the implications for future telescopes and surveys.
