By a symbolic extension of a topological dynamical system (X,T) we mean an extension of (X,T) which is a subshift over a finite alphabet. The existence and the entropy of these extensions are related to the convergence of the metric entropy of (X,T) computed at finer and finer scales. T. Downarowicz and S. Newhouse have conjectured that any C^r with r>1 map on a compact manifold admits symbolic extensions. In this talk we will discuss the case of surface maps.