The spatially-unresolved sub-parsec region of quasars (rapidly accreting supermassive black holes) is a dynamic environment where the most important processes related to BH accretion and feedback are taking place. Studying this region observationally, however, requires somewhat different approaches that are not hurdled by the spatial resolution requirement. A hallmark characteristic of quasars is their ubiquitous variability over a wide range of wavelengths and timescales from intra-day to decades, which provides unique and critical constraints on the structure, dynamics, and radiative processes in the innermost emitting regions of accreting SMBHs that are otherwise difficult to probe. I will give a brief overview on variability studies to understand the inner structures of quasars, with several examples such as the measurement of the sizes of the accretion disk and the gaseous broad-line region with light echos, and the discovery and characterization of extreme variability events that challenge current accretion theories. Finally I will discuss the prospects of advancing quasar science in the upcoming time-domain era of LSST.