Over a century ago, Boltzmann and others provided a microscopic understanding for the tendency of entropy to increase. But this understanding relies ultimately on an empirical fact about cosmology: the early universe had a very low entropy. Why was it like that? Cosmologists aspire to provide a dynamical explanation for the observed state of the universe, but have had very little to say about the dramatic asymmetry between early times and late times. I will argue that the search for a natural explanation for the observed breakdown of time-reversal symmetry in cosmology leads us directly to interesting conclusions about inflation, quantum gravity, and the multiverse.