Mesoscopic magnetic structures play an increasingly important role in magnetic storage technology, magnetic sensors, non-volatile random access memories, and "magneto-electronics" in general. Lithography-type processes for making such structures, though having been quite successful, will not be addressed in this talk. Rather, typical surface science approaches, involving adsorption, surface diffusion, epitaxial growth phenomena, and self-organisation will be exploited to produce and characterize mesoscopic magnetic structures. For example, magnetic wires may be made by step edge decoration on stepped single crystal surfaces by tuning surface diffusion. They form chains of long segments, connected by weak links. These structures resemble Ising chains, with magnetic properties determined by a gradual approach to thermodynamic equilibrium. Magnetic dots may be created by exploiting localized adsorption on reconstructed surfaces. It will be demonstrated, how magnetic pillars with a height-to-diameter ration of 2:1 can be grown on such a template and that such structures may perhaps overcome the "superparamagnetic barrier" in magnetic storage technology.