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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..The size of the matrix,N,endows a matrix model with a small parameter,1/N,and its perturbative expansion can be reorganised as series in 1/N.The leading order contribution represents planar surfaces.As the leading order is summable,matrix models undergo a phase transition to a continuum theory of random,infinitely refined,surfaces.In higher dimensions matrix models generalise 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.I will present an overview of these results and discuss their implications to statistical mechanics,integrable systems,quantum field theory,random discrete geometries and probability theory.