  The purpose of this review is to discuss recent developments occurring at the
interface of cosmology with string and M-theory. We begin with a short review
of 1980s string cosmology and the Brandenberger-Vafa mechanism for explaining
spacetime dimensionality. It is shown how this scenario has been modified to
include the effects of p-brane gases in the early universe. We then introduce
the Pre-Big-Bang scenario (PBB), Ho\v{r}ava-Witten heterotic M-theory and the
work of Lukas, Ovrut and Waldram, and end with a discussion of large extra
dimensions, the Randall-Sundrum model and Brane World cosmologies.
