For many years physicists thought small structures would be nearly ideal systems in which to explore and manipulate magnetic interactions. On a small enough length scale the interactions between individual atomic spins cause their magnetic moments to align in the ordered pattern of a single domain, without the complication of domain walls separating regions of varying orientation. For particle sizes at or below that of a single domain, many theoretical models of dynamical behavior predict simple, stable magnets with controllable classical properties. However, as with advances in semiconductor physics, the process of miniaturizing magnetic materials has unexpectedly revealed fascinating new classical and quantum mechanical phenomena. Even the simplest magnetic system, the isolated single-domain particle, exhibits a wealth of exotic behavior that pushes us to the limits of our present understanding of the fundamentals of magnetism. The study of ever smaller magnets is pushing us to the limits of our understanding of magnetism, providing new headaches for the technologist and new opportunities for the researcher investigating magnetism at the atomic level. © 1995, American Institute of Physics. All rights reserved.