  Magnetically-doped graphene systems are potential candidates for application
in future spintronic devices. A key step is to understand the pairwise
interactions between magnetic impurities embedded in graphene that are mediated
by the graphene conduction electrons. A large number of studies have been
undertaken to investigate the indirect exchange, or RKKY, interactions in
graphene. Many of these studies report a decay rate faster than expected for a
2-dimensional material and the absence of the usual distance dependent
oscillations. In this review we summarize the techniques used to calculate the
interaction and present the key results obtained to date. The effects of more
detailed parameterisations of the magnetic impurities and graphene host are
considered, as are results obtained from ab initio calculations. Since the fast
decay of the interaction presents an obstacle to spintronic applications, we
focus in particular on the possibility of augmenting the interaction range by a
number of methods including doping, spin precession and the application of
strain.
