  Magnetic materials and nanostructures based on carbon offer unique
opportunities for future technological applications such as spintronics. This
article reviews graphene-derived systems in which magnetic correlations emerge
as a result of reduced dimensions, disorder and other possible scenarios. In
particular, zero-dimensional graphene nanofragments, one-dimensional graphene
nanoribbons, and defect-induced magnetism in graphene and graphite are covered.
Possible physical mechanisms of the emergence of magnetism in these systems are
illustrated with the help of computational examples based on simple model
Hamiltonians. In addition, this review covers spin transport properties,
proposed designs of graphene-based spintronic devices, magnetic ordering at
finite temperatures as well as the most recent experimental achievements.
