Most, if not all, galaxies contain supermassive black holes (SMBHs) at their centers. These are black holes millions or billions of times the mass of the Sun, and they are believed to play a significant role in the formation and evolution of massive galaxies. However, many key unanswered questions about SMBHs remain. What factors drive their rapid growth? Could the energy released by accreting SMBHs be the key to understanding why very massive galaxies tend to have little star formation? I will describe how I have used computational models of galaxy evolution to study these questions and gain insight into the SMBHs and their host galaxies evolve together and influence each other over the course of their lifetimes.