While astronomers are on the cusp of detecting the earliest galaxies and tracing galaxy evolution over a Hubble time, we remain baffled by the present-day dichotomy between disky galaxies that are forming stars and spheroidal galaxies that are not. The key is to find galaxies in transition from one class to the other, preferably in the nearby universe where we have access to an abundance of spatially resolved and multi-wavelength data. We have now identified thousands of such "post-starburst galaxies" whose dynamics, stellar populations, star clusters, and morphologies are consistent with recent, dramatic evolution. This evolution often arises from galaxy-galaxy interactions and is connected in complex ways to the galaxy's central, supermassive black hole and newly formed stars. For reasons that we are working to explain, these galaxies are the preferred sites for stellar tidal disruptions by supermassive black holes, a surprising link between sub-pc and kpc scales reminiscent of the black hole-galaxy bulge mass relation. Regardless of the physical mechanism that drives it, the preference for certain host galaxies is a valuable tool for rapidly classifying these rare astrophysical transients, especially in the era of Vera Rubin Observatory's Legacy Survey of Space and Time.