  Random matrix models encode a theory of random two dimensional surfaces with
applications to string theory, conformal field theory, statistical physics in
random geometry and quantum gravity in two dimensions. The key to their success
lies in the 1/N expansion introduced by 't Hooft. Random tensor models
generalize random matrices to theories of random higher dimensional spaces. For
a long time, no viable 1/N expansion for tensors was known and their success
was limited. A series of recent results has changed this situation and the
extension of the 1/N expansion to tensors has been achieved. We review these
results in this paper.
