ABSTRACT Although there has been much progress in understanding how galaxies evolve, we still do not understand how and when they stop forming stars and become quiescent. We address this by applying our galaxy spectral energy distribution models, which incorporate physically motivated star formation histories (SFHs) from cosmological simulations, to a sample of quiescent galaxies at . A total of 845 quiescent galaxies with multi-band photometry spanning rest-frame ultraviolet through near-infrared wavelengths are selected from the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS) data set. We compute median SFHs of these galaxies in bins of stellar mass and redshift. At all redshifts and stellar masses, the median SFHs rise, reach a peak, and then decline to reach quiescence. At high redshift, we find that the rise and decline are fast, as expected, because the universe is young. At low redshift, the duration of these phases depends strongly on stellar mass. Low-mass galaxies ( ) grow on average slowly, take a long time to reach their peak of star formation ( Gyr), and then the declining phase is fast ( Gyr). Conversely, high-mass galaxies ( ) grow on average fast ( Gyr), and, after reaching their peak, decrease the star formation slowly ( ). These findings are consistent with galaxy stellar mass being a driving factor in determining how evolved galaxies are, with high-mass galaxies being the most evolved at any time (i.e., downsizing). The different durations we observe in the declining phases also suggest that low- and high-mass galaxies experience different quenching mechanisms, which operate on different timescales.