Magnetism in low dimensionality

The collective creativity of those working in the field of surface magnetism has stimulated an impressive range of advances. Once wary, theorists are now eager to enter the field. The present article attempts to take a snapshot of where the field has been, with an eye to the more speculative issue of where it is going. Selective examples are used to highlight three general areas of interest: (i) characterization techniques, (ii) materials properties, and (iii) theoretical/simulational advances. Emerging directions are identified and discussed, including laterally confined nanomagnetism and spintronics.