  A bouncing cosmology with an initial matter-dominated phase of contraction
during which scales which are currently probed with cosmological observations
exit the Hubble radius provides a mechanism alternative to inflation for
producing a nearly scale-invariant spectrum of cosmological perturbations. In
this review article I first discuss the evolution of cosmological fluctuations
in the matter bounce scenario, and then discuss various attempts at realizing
such a scenario. Observational signatures which will allow the matter bounce to
be distinguished from the inflationary paradigm are also discussed.
