  Matrix models are a highly successful framework for the analytic study of
random two dimensional surfaces with applications to quantum gravity in two
dimensions, string theory, conformal field theory, statistical physics in
random geometry, etc. Their success relies crucially on the so called 1/N
expansion introduced by 't Hooft.
  In higher dimensions matrix models generalize to tensor models. In the
absence of a viable 1/N expansion tensor models have for a long time been less
successful in providing an analytically controlled theory of random higher
dimensional topological spaces. This situation has drastically changed
recently. Models for a generic complex tensor have been shown to admit a 1/N
expansion dominated by graphs of spherical topology in arbitrary dimensions and
to undergo a phase transition to a continuum theory.
