The spatially-unresolved sub-parsec region of quasars (rapidly accreting supermassive black holes) is a dynamic environment where the most energetic processes related to BH accretion and feedback are taking place. Studying this region observationally, however, requires somewhat different approaches that are not limited by the spatial resolution requirement. A hallmark characteristic of quasars is variability, which provides critical constraints on the structure, dynamics, and radiative processes in the innermost emitting regions of accreting SMBHs, without the need to resolve these regions spatially. I will present some recent work of our group on quasar variability, focusing on extreme variability quasars and reverberation mapping to measure the broad-line region size and BH masses. I will also briefly discuss the prospects of quasar variability studies in the upcoming era of the Large Synoptic Survey Telescope.