Localization methods express the partition functions of Chern--Simons--matter theories in terms of matrix models. By the AdS/CFT correspondence, they correspond to superstring and M-theory partition functions in certain AdS backgrounds. In this talk I will summarize the different methods that have been developed to study the matrix models at large N, and then I will explain the implications for M-theory and superstrings. In particular, I will discuss how this matrix model makes it possible to calculate non-perturbative effects in string theory and M-theory.