The Weil-Petersson model is a beautiful probabilistic model allowing to study random hyperbolic surfaces, which was first popularised by Mirzakhani and is now at the center of a very active field of study. I will gently introduce this model, and present techniques that can be used to count closed geodesics on these random hyperbolic surfaces. Notably, I will present joint work with Nalini Anantharaman allowing to count non-simple closed geodesics, including new coordinates on Teichmüller space.