  We propose a short overview of a few selected issues of magnetism in reduced
dimensions, which are the most relevant to set the background for more
specialized contributions to the present Special Issue. Magnetic anisotropy in
reduced dimensions is discussed, on a theoretical basis, then with experimental
reports and views from surface to single-atom anisotropy. Then conventional
magnetization states are reviewed, including macrospins, single domains,
multidomains, and domain walls in stripes. Dipolar coupling is examined for
lateral interactions in arrays, and for interlayer interactions in films and
dots. Finally thermally-assisted magnetization reversal and superparamagnetism
are presented. For each topic we sought a balance between well established
knowledge and recent developments.
