The (unique) maximally extended D=11 supermembrane theory stands out as a candidate for the non-perturbative unification of superstring theory. In this talk I will review some basic features, in particular the light-cone gauge reformulation of the theory as the N-->\infty limit of the maximally supersymmetric SU(N) matrix model, and present new evidence for the existence of the N-->\infty limit, using a path integral formulation. I will also touch on several open issues, such as the construction of supermembrane vertex operators.