Post-starburst (or “E+A”) galaxies are in transition between star-forming galaxies and early-types, and represent a clear path for galaxies to transform from star-forming to quiescence. Many show signs of a recent galaxy-galaxy merger and a newly-evolved stellar bulge, and most have LINER-like emission, which may indicate low luminosity AGN activity. Thus, the study of this short-lived phase of galaxy evolution can address the connections among mergers, star formation history, and the evolution of the nucleus as a galaxy evolves onto the red sequence. Surprisingly, we have discovered that many these galaxies, which are not currently forming stars, have significant reservoirs of molecular gas, which may fuel the central, supermassive black hole after the starburst has ended. We have also found that post-starburst galaxies host a disproportionate number of Tidal Disruption Events, in which a star is accreted onto the black hole. The recent starburst in these galaxies allows us to put strong constraints on the details of their recent star formation histories, and to place them on a timeline post-burst. I will discuss these results and other new work detailing how their stellar populations, gas content, and black hole properties evolve.