The curve graph of a surface has a vertex for each curve on the surface and an edge for each pair of disjoint curves. Although it deals with very simple objects, it has become classic in low-dimensional topology and geometry, as it enjoys some interesting properties and has connections with several questions arising in this subject. Yet this graph is more complicated than it may look from its definition, and often forces people to approach it only from the point of view of coarse geometry, which means looking at wide portions of this graph, disregarding what happens at a smaller scale. In particular I will explain how one can get an idea of how do the ‘quasi-geodesics’ of the curve graph look like: this requires introducing a kind of pictures one can draw on a surface, which in the fantasy of Bill Thurston looked like a railway network.