The main question I will address in my talk is what shuts down star formation in galaxies.  I will highlight recent observational work on outflowing galactic-scale winds and the potential impact of these winds on star formation in galaxies.  I will present new work on which galaxies host accreting supermassive black holes and the lack of evidence for these black holes impacting their host galaxies.  Finally, I will show what galaxies look like when their star formation is being shut down and what we can learn from the morphological transformations they undergo during this process.  At the end I will briefly mention a new Keck survey I am co-leading to study even more distant galaxies with large, statistical samples.