Galaxies mark the nexus between the "micro" scales of individual stars and black holes, and the "macro" scales of the "cosmic web", the large scale structure in which galaxies are embedded. Modeling the physics of galaxy formation is therefore one of the greatest challenges in astrophysics today because of the enormous range of scales involved and the diversity of physical processes that are important. However, models have made enormous progress in the past few years towards explaining a variety of observations and identifying a set of essential physical processes that shape the observable properties of galaxies. I will review the successes and some of the failures of state-of-the-art cosmological models of galaxy formation when confronted with an array of observations and discuss what we have learned from these results about the physics that drive galaxy evolution. I will focus on understanding the link between the structural and morphological properties of galaxies and their formation histories.