Two aspects of low-dimensional magnetism are discussed: the spin-dependent quantization effects in perfect two-dimensional single crystal layers and the magnetic domain structure of submicron magnetic patterns. Both require high lateral resolution and surface sensitivity. This is provided by spin-polarized low energy electron microscopy (SPLEEM) and X-ray magnetic circular dichroism photoemission electron microscopy (XMCDPEEM). (c) 2004 Elsevier B.V. All rights reserved.