  Spin orbit coupling changes graphene, in principle, into a two-dimensional
topological insulator, also known as quantum spin Hall insulator. One of the
expected consequences is the existence of spin-filtered edge states that carry
dissipationless spin currents and undergo no back-scattering in the presence of
non-magnetic disorder, leading to quantization of conductance. Whereas, due to
the small size of spin orbit coupling in graphene, the experimental observation
of these remarkable predictions is unlikely, the theoretical understanding of
these spin-filtered states is shedding light on the electronic properties of
edge states in other two-dimensional quantum spin Hall insulators. Here we
review the effect of a variety of perturbations, like curvature, disorder, edge
reconstruction, edge crystallographic orientation, and Coulomb interactions on
the electronic properties of these spin filtered states.
