Irradiating solids with energetic particles is usually thought to introduce disorder, normally an undesirable phenomenon. But recent experiments on electron or ion irradiation of various nanostructures demonstrate that it can have beneficial effects and that electron or ion beams may be used to tailor the structure and properties of nanosystems with high precision. Moreover, in many cases irradiation can lead to self-organization or self-assembly in nanostructures. In this review we survey recent advances in the rapidly evolving area of irradiation effects in nanostructured materials, with particular emphasis on carbon systems because of their technological importance and the unique ability of graphitic networks to reconstruct under irradiation. We dwell not only on the physics behind irradiation of nanostructures but also on the technical applicability of irradiation for nanoengineering of carbon and other systems.