While much effort has been expended to detect the earliest galaxies and to follow their evolution to z~0, astronomers remain baffled by the present-day dichotomy between disky, star forming (aka late-type) galaxies and quiescent, spheroidal (aka early-type) galaxies. Finding galaxies in transition from one class to the other, whose spectra indicate intense recent star formation that has now ended, is key.  We have identified thousands of such "post-starburst galaxies" and discovered that they are often the products of late-type galaxy-galaxy mergers. Their current kinematics, stellar populations, and morphologies are consistent with late- to early-type galaxy evolution. I will discuss recent work that further demonstrates the importance of these galaxies in the study of galaxy evolution. In particular, we have shown that their molecular gas fractions decline rapidly in time after the starburst ends and in a manner consistent with feedback processes. Furthermore, we have determined that tidal disruption events, in which a star is disrupted by the supermassive black hole in a galaxy's center, favor post-starburst galaxies by factors of tens to hundreds. Like the well-known black hole-bulge mass correlation, this surprising connection between the properties of a galaxy on kpc scales and its supermassive black hole on pc scales requires explanation.