The ekpyrotic/cyclic model proposes that time did not begin at the big bang, but that the universe previously underwent a long period of slow contraction. It is during this contracting phase that a scale-invariant spectrum of density perturbations is generated. There is no inflationary era after the big bang, and thus the model is a candidate alternative to the standard inflationary paradigm. However there is a key observational difference: inflation also predicts a nearly scale-invariant spectrum of gravitational waves, while the ekpyrotic model does not. In this talk I will review some of the essential elements of ekpyrotic/cyclic cosmology, as well as describe recent work on parallels and contrasts with inflationary cosmology.