  The two-dimensional electron systems in graphene and in topological
insulators are described by massless Dirac equations. Although the two systems
have similar Hamiltonians, they are polar opposites in terms of spin-orbit
coupling strength. We briefly review the status of efforts to achieve long spin
relaxation times in graphene with its weak spin-orbit coupling, and to achieve
large current-induced spin polarizations in topological-insulator surface
states that have strong spin-orbit coupling. We also comment on differences
between the magnetic responses and dilute-moment coupling properties of the two
systems, and on the pseudospin analog of giant magnetoresistance in bilayer
graphene.
