The goal of this talk is to present the wall-crossing formula (WCF) introduced by Kontsevich and Soibelman and a class of Riemann-Hilbert problems naturally associated. The WCF describes a special behaviour of some counting invariants depending on a parameter space in a piece-wise constant way. I will recall how this formula appears with an explicit example of a moduli space of quadratic differentials and I will present the solution of a simple instance of the Riemann-Hilbert problem.