Jaroslav Fabian and his group investigate topological properties of models that describe graphene on realistic substrates, which induce proximity spin-orbit coupling in graphene. Discussing how quantum anomalous Hall and quantum spin Hall effects arise in graphene, we also show how graphene with staggered intrinsic spin-orbit coupling, despite being topologically trivial, exhibits protected edge states. The spin character and robustness of the modes is best exhibited on a finite flake, which shows that the edge states have zero g-factor, carry a pure spin current in the crossection of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges.