In a 2008 paper, Fomin, Shapiro and Thurston constructed a quiver given a triangulated bordered surface. It turns out that the class of quivers arising from this construction gives us almost all the mutation-finite quivers, only with minor exceptions. In this talk, we will review the notions of quivers and their mutations. We will then introduce the triangulations of surfaces, associate to each triangulated surface a quiver and study how flips of triangulation correspond to quiver mutations. We will finally see how quivers from surfaces are involved in the classification of mutation-finite quivers.