Multidimensional integrals of the form $int prod_{i = 1}^N dx_i w(x_i) prod_{1 leq i < j leq N} R(x_i,x_j)$ can be considered as a generalization of the 1-hermitian matrix model (for which $R(x_i,x_j) = (x_i - x_j)^2$). They appear in many problems of theoretical physics, not always related to random matrix theory: statistical physics on the random lattice (O(n) loop models or ADE height models), topological strings (ABJM matrix model, ...), Chern-Simons theory (torus knots, Seifert manifolds, ...), conformal field theory (conformal blocks of Liouville theory), etc. For all those models, I will show (at least at the formal level) that the all-order large N expansion is governed by the same topological recursion which has been found by Eynard for the 1-hermitian matrix model, and discuss some applications of this result.