Astronomy Colloquium

Dark matter halos are the fundamental building blocks in the growth of structure and they provide the framework for our modern understanding of galaxy formation. I will discuss the current state of the art in our understanding of the connection between galaxy properties and their dark matter hosts over a range of masses and redshifts. In the context of a given cosmological model, I will show how the galaxy-halo relation can be tightly constrained at low redshift, and how it can be used to infer the full star formation histories of galaxies. This model for the co-evolution of galaxies and LCDM halos is in excellent agreement with a wide range of data, including the evolution of the stellar mass function, galaxy clustering statistics, and the statistics of satellites around Milky Way mass hosts. The faintest dwarf galaxies still present challenges to this picture, and may hold the key to new insight into galaxy formation or the properties of dark matter on small scales.