  Ekpyrotic and cyclic cosmologies provide theories of the very early and of
the very late universe. In these models, the big bang is described as a
collision of branes - and thus the big bang is not the beginning of time.
Before the big bang, there is an ekpyrotic phase with equation of state w=P/rho
>> 1 (where P is the average pressure and rho the average energy density)
during which the universe slowly contracts. This phase resolves the standard
cosmological puzzles and generates a nearly scale-invariant spectrum of
cosmological perturbations containing a significant non-gaussian component. At
the same time it produces small-amplitude gravitational waves with a blue
spectrum. The dark energy dominating the present-day cosmological evolution is
reinterpreted as a small attractive force between our brane and a parallel one.
This force eventually induces a new ekpyrotic phase and a new brane collision,
leading to the idea of a cyclic universe. This review discusses the detailed
properties of these models, their embedding in M-theory and their viability,
with an emphasis on open issues and observational signatures.
