In the next decade, astronomers will map out enormous volumes of our Universe to unprecedented precision. Subtle features in these maps can reveal the presence of new particles, the nature of dark matter and dark energy, and even the mechanism for cosmic inflation. We will also learn about the formation of galaxies and the cosmic web. The key to achieving these goals is a detailed understanding of structure formation, the gravitational collapse of seed density perturbations into the large-scale structure of the Universe we see today. I will review the history of structure in our Universe, recent innovations in the theory of structure formation, and how they can be used to identify new physics in cosmological datasets.