Eternal Inflation, past and future

Cosmological inflation, if it occurred, radically alters the picture of the `big bang', which would merely point to reheating at the end of inflation. Moreover, this reheating may be only local, so that inflation continues elsewhere and forever, continually spawning big-bang-like regions. This chapter reviews this idea of `eternal inflation', then focuses on what this may mean for the ultimate beginning of the universe. In particular, I will argue that given eternal inflation, the universe may be free of a cosmological initial singularity, might be eternal (and eternally inflating) to the past, and might obey an interesting sort of cosmological time-symmetry.