FastSpecFit models the observed-frame optical spectroscopy and broadband photometry of extragalactic targets using physically grounded stellar continuum and emission-line templates. The code handles data from the Dark Energy Spectroscopic Instrument (DESI) Survey, which is amassing spectrophotometry for an unprecedented 40 million extragalactic targets, although the algorithms are general enough to accommodate other upcoming, massively multiplexed spectroscopic surveys. FastSpecFit extracts nearly 800 observed- and rest-frame quantities from each target, including light-weighted ages and stellar velocity dispersions based on the underlying stellar continuum; line-widths, velocity shifts, integrated fluxes, and equivalent widths for nearly 40 rest-frame ultraviolet, optical, and near-infrared emission lines arising from both star formation and active galactic nuclear activity; and K-corrections and rest-frame absolute magnitudes and colors. Moreover, FastSpecFit is designed with speed and parallelism in mind, enabling it to deliver robust model fits to tens of millions of targets.