Galaxies form and evolve within hierachically growing dark matter halos. While halo formation is simple, galaxy formation within halos has proven to be a very hard problem to understand. I will discuss how we use the stellar mass function, measures of the star formation rate, and measures of the merger rate to attempt to construct a picture of the mass assembly of galaxies. I will also discuss how the shape of the stellar mass function provides insight into the processes that shape galaxies, such as feedback, accretion, and merging; and how a relation between stellar mass and halo mass can be arrived at and what we can learn from it.