  We consider conditions under which a universe contracting towards a big
crunch can make a transition to an expanding big bang universe. A promising
example is 11-dimensional M-theory in which the eleventh dimension collapses,
bounces, and re-expands. At the bounce, the model can reduce to a weakly
coupled heterotic string theory and, we conjecture, it may be possible to
follow the transition from contraction to expansion. The possibility opens the
door to new classes of cosmological models. For example, we discuss how it
suggests a major simplification and modification of the recently proposed
ekpyrotic scenario.
