  The ubiquitous variability of quasars across a wide range of wavelengths and
timescales encodes critical information about the structure and dynamics of the
circumnuclear emitting regions that are too small to be directly resolved, as
well as detailed underlying physics of accretion and feedback processes in
these active supermassive black holes. We emphasize the importance of studying
quasar variability with time-domain spectroscopy, focusing on two science
cases: (1) reverberation mapping (RM) to measure the broad-line region sizes
and black hole masses in distant quasars; (2) spectroscopic follow-up of
extreme variability quasars that dramatically change their continuum and
broad-line flux within several years. We highlight the need for dedicated
optical-infrared spectroscopic survey facilities in the coming decades to
accompany wide-area time-domain imaging surveys, including: (1) the next phase
of the Sloan Digital Sky Survey (SDSS-V; ~2020-2025), an all-sky, time-domain
multi-object spectroscopic survey with 2.5m-class telescopes; (2) the planned
Maunakea Spectroscopic Explorer, a dedicated 10m-class spectroscopic survey
telescope with a 1.5 sq. deg field-of-view and multiplex of thousands of fibers
in both optical and near-IR (J+H) to begin operations in 2029; (3) the
Time-domain Spectroscopic Observatory (TSO), a proposed Probe-class ~1.3m
telescope at L2, with imaging and spectroscopy (R=200, 1800) in 4 bands (0.3 -
5 micron) and rapid slew capability to 90% of sky, which will extend the
coverage of Hbeta to z=8.
