The symmetric simple exclusion process (SSEP) is one of the fundamental models of stochastic interacting particle systems. Interested in transport in disordered media, we consider a very large family of random graphs in R^d with random weights (conductances), modeling a medium which is microscopically disordered but macroscopically homogeneous from a statistical viewpoint. This class includes e.g. the supercritical percolation cluster on Z^d or other lattices, the Delaunay triangulation of a point process, the Boolean model, the random connection model, the complete graph of a point process (all with random conductances). We then consider the SSEP on these graphs. We discuss its graphical construction and the quenched hydrodynamic limit in path space mainly based on homogenization and duality. For some special cases we present results on the equilibrium fluctuations.