Given a marked bordered surface S and a triangulation T one can associate a Cluster Algebra C(S,T), which is a combinatorically defined algebra on a set of generators. In the classical setting, where marked points lie only on the boundary of S, arcs on the surface correspond to polynomials in the Cluster Algebra and one can associate the so-called snake graphs to these arcs. In this talk we will first explain how one can generalize this construction when one allows marked points in the interior of the surface and then explain how this new machinery can be used to resolve crossing of arcs (crossing of snake graphs) on the surface.