  Efforts to understand and map the possible explanations for the late time
acceleration of the universe have led to a broad range of suggestions, ranging
from the cosmological constant and straightforward dark energy, to exotically
coupled models, to infrared modifications of General Relativity. If we are to
uncover which, if any, of these approaches might provide a serious answer to
the problem, it is crucial to understand the constraints that theoretical
consistency places on the models, and on the regimes in which they make
predictions. In this talk, delivered as an invited plenary lecture at the Dark
Side of the Universe conference in Kyoto, Japan, I briefly describe some modern
attempts to carry out this program and some of the more interesting ideas that
have emerged. As an example, I use the Galileon model, discussing how the
Vainshtein mechanism occurs, and how a number of these theoretical problems
arise around such backgrounds.
