This chapter discusses the magnetic nature of intrinsic and irradiation-induced defects in carbon systems. It is found that when an energetic particle such as an electron or ion hits a material, different mechanisms of damage creation can work. Because of the open structure of carbon nanotubes and low density of the nanotube samples, the damage formation in carbon nanotubes is quite different from that observed in most other solids. The total energy obtained from the periodic model calculation includes the interaction of the defect with its images. The periodic model is ideal if one is interested in the ground-state properties of neutral defects, which weakly perturb the surrounding lattice. The abundance of open space in nanotubes suggests that the interstitial atom can also be treated as an adatom adsorbed onto the nanotube surface. It is found that migration of adatoms on nanotubes is important because this issue is directly related to the stability of magnetic defects.