I will explain how some recent progress on the Wheeler-DeWitt equation makes possible the systematic development of quantum cosmology in the canonical formulation. The cosmological wavefunctions are automorphic forms, and the Wheeler-DeWitt equation reduces to a dynamical equation on moduli space, so that quantum cosmology is equivalent to "automorphic dynamics". I will describe in detail this equivalence in the simple context of pure three-dimensional gravity and comment on how these ideas should generalize to higher dimensions and to our universe.