Identifying key physical processes responsible for bringing galactic star formation to a halt is one of the most important unresolved questions in the field of galaxy evolution. I will present an overview of our recent studies, where we apply a combination of correlation analysis and simple machine learning techniques to determine physical mechanisms most likely responsible for ceasing star formation in massive galaxies. By comparing state-of-the-art cosmological simulations and survey observations on equal footing, we make a convincing case for star formation being suppressed by supermassive black holes between redshift z=4 and the local Universe. Zooming in on the supermassive black holes themselves, I will also discuss the current landscape of black hole angular momentum measurements and the potential for constraining their cosmological growth with future generation broadband X-ray observatories.