Abstract: The well-known Borde-Guth-Vilenkin Theorem shows that inflationary spacetimes are generically geodesically past-incomplete, necessitating the existence of a pre-inflationary boundary of some sort, possibly singular. In this talk, I discuss the generalization of the BGV theorem to spactimes beyond inflation, including inhomogeneous and cyclic models. I argue that the cyclic model proposed by Ijjas and Steinhardt is geodesically incomplete, and that an asymptotically de Sitter version of Penrose's Conformal Cyclic Cosmology is either past- or future-incomplete.