Every cluster algebra has an associated 'scattering diagram': an affine space endowed with a (possibly very complicated) collection of 'walls'. The structure of this scattering diagram encodes essential information about the cluster algebra's exchange graph, Laurent coefficients, and theta functions. In this talk, I will discuss an ongoing project with Nathan Reading and Shira Viel to construct a scattering diagram associated to a triangulable marked surface. The affine space may be identified with the set of certain `measured laminations' on the surface, and the walls may be identified with certain forbidden subgraphs embedded in the surface, which we call `barricades'.