The distribution of galaxies on large scales is a sensitive probe of fundamental physics. In particular, the structure of this distribution depends on properties of dark matter and the dynamics of the early universe. Understanding this dependence, however, is a challenging task because the observed galaxy distribution is modulated by a variety of non-linear effects. I will present new theoretical tools that have allowed for a systematic analytic description of these effects. These tools play a central role in a new program of extracting cosmological information from large scale galaxy surveys. I will share some results of this program from several independent analyses of the public data from the Baryon acoustic Oscillation Spectroscopic Survey. These results include new limits on primordial non-Gaussianity, parity violation in the cosmological initial conditions, and novel constraints on dark matter models.