A comprehensive review and state of the art in the field of surface, interface, and thin-film magnetism is presented. New growth techniques which produce atomically engineered novel materials, special characterization techniques to measure magnetic properties of low-dimensional systems, and computational advances which allow large complex calculations have together stimulated the current activity in this field and opened new opportunities for research. The current status and issues in the area of material growth techniques and physical properties, characterization methods, and theoretical methods and ideas are reviewed. A fundamental understanding of surface, interface, and thin-film magnetism is of importance to many applications in magnetics technology, which is also surveyed. Questions of fundamental and technological interest that offer opportunities for exciting future research are identified.