Abstract We investigate the properties of galaxies as they shut off star formation over the 4 billion years surrounding peak cosmic star formation. To do this, we categorize ∼7000 galaxies from 1 <  z  < 4 into 90 groups based on the shape of their spectral energy distributions (SEDs) and build composite SEDs with R  ∼ 50 resolution. These composite SEDs show a variety of spectral shapes and also show trends in parameters such as color, mass, star formation rate, and emission-line equivalent width. Using emission-line equivalent widths and strength of the 4000 Å break, , we categorize the composite SEDs into five classes: extreme emission line, star-forming, transitioning, post-starburst, and quiescent galaxies. The transitioning population of galaxies shows modest H α emission (EW REST  ∼ 40 Å) compared to more typical star-forming composite SEDs at log 10 ( M / M ⊙ ) ∼ 10.5 (EW REST  ∼ 80 Å). Together with their smaller sizes (3 kpc vs. 4 kpc) and higher Sérsic indices (2.7 vs. 1.5), this indicates that morphological changes initiate before the cessation of star formation. The transitional group shows a strong increase of over 1 dex in number density from z  ∼ 3 to z  ∼ 1, similar to the growth in the quiescent population, while post-starburst galaxies become rarer at z  ≲ 1.5. We calculate average quenching timescales of 1.6 Gyr at z  ∼ 1.5 and 0.9 Gyr at z  ∼ 2.5 and conclude that a fast-quenching mechanism producing post-starbursts dominated the quenching of galaxies at early times, while a slower process has become more common since z  ∼ 2.