This survey of major themes, essential results, and open questions in the field of carbon nanostructure magnetism focused on three main areas of current research activity: the intrinsic magnetism of carbon-based nanomaterials, magnetism caused by impurities embedded into these materials, and their interest as media for spin transport. Discoveries continue to be made in each of these three domains. Far from presenting a closed body of knowledge, the arena of carbon nanostructure magnetism is wide open in many directions, and its future course is difficult to chart. As it reaches into a multiplicity of very diverse disciplines, such as biomedicine, spintronics or quantum information processing, its locus within nanoscience keeps changing.

Various results in this field have given rise to extensive debate and, in some cases, ongoing controversy. Thus, carbon-based magnetism in the sense of intrinsic magnetic effects is an embattled zone of current materials science. These effects involve magnetism due to unsaturated or incompletely saturated edge structures of carbon nano systems, or due to vacancies and voids in the carbon network, or topological defects, as discussed in Chapter 7. In monolayer graphene, but also in other systems derived from this prototype, Lieb's theorem provides the conceptual frame for the quantitative assessment of the resulting magnetic order. Theoretical and computational predictions of these phenomena abound, and some recent experimental findings are in accordance with these predictions, as pointed out in Chapter 7. However, none of the presently available experimental findings related to intrinsic carbon magnetism have been greeted with unanimous acceptance by the scientific community. Even if the existence of ordered magnetic substructures due to edge effects would be experimentally validated beyond doubt, its use in technology would set very high standards of materials engineering. Specifically, it would necessitate designing carbon nanostructures with atomic precision, which is not feasible by use of current routine fabrication modes.