
Topological defects play a major role in magnetic phase transitions (e.g. domain walls in the Ising model and vortices in the XY model). They also strongly influence the dynamics of magnetization away from equilibrium. Classic examples are Walker's problem of a moving Bloch domain wall in one dimension and more recent studies of a magnetic vortex confined to a disk. After a brief overview of these cases, I will describe some of the modern problems: the dynamics of an array of defects (a skyrmion crystal) and that of a line defect (a domain wall in a thin film). In all of these examples, the dynamics of magnetization is dominated by the effects of the Berry phase associated with non-coplanar trajectories of spins.