Cluster algebras of type A are subalgebras of a field of rational functions in several variables. They are generated by a distinguished set of generators, the cluster variables, which correspond to the diagonals of a regular polygon. Musiker and Schiffler gave an expansion formula for the cluster variables in terms of perfect matchings of some labeled graphs, called snake graphs, that are recursively constructed from the polygon by gluing together elementary pieces called tiles. In this talk, I will introduce the combinatorics of snake graphs, and explain the cluster expansion formula of Musiker and Schiffler. In conclusion, I will present an extension of the construction to cluster algebras of type B and C.