Grothendieck's dessins d'enfant and matrix models

The technique of random matrix models turned out to be well suited for describing generating functions of numbers of Grothendieck's dessins d'enfant of a given structure. I describe some recent advances in this field and generalizations of these models to description of "hypergeometric Hurwitz numbers"corresponding to mappings $\sum_{g}$ $\rightarrow$ $CP^1$ branched over a fixed number of points in the projective plane.