Galaxies are complicated beasts - many physical processes operate simultaneously, and over a huge range of scales in space and time. As a result, accurately modeling the formation and evolution of galaxies over the lifetime of the universe presents tremendous technical challenges. In this talk I will describe some of the important unanswered questions about galaxy formation, discuss in general terms how we simulate the formation of galaxies on a computer, and present simulations (and accompanying published results) that the Enzo collaboration has recently done on the Blue Waters supercomputer.