The bidimensionnal character of thin magnetic films deposited on single-crystal substrates, together with the occurrence of singular crystallographic structures, often confer on these systems electronic properties that cannot be found in bulk solids. For example, thin Ni layers deposited on Cu(001) present a perpendicular magnetic anisotropy in a very wide thickness range. We will show that this can be explained by a distorted structure of Ni, originating from the strain induced by the epitaxy on the Cu substrate. In this field of 2D magnetism, nanostructures are now investigated. Thin Fe layers on MgO(001) were cut into stripes by the "atomic saw" method: a compression of the substrate induces a dislocation slipping which saws both the substrate and the Fe film in regular and separated ribbons. The observed perpendicular to the stripes magnetization easy axis will be explained by a structural relaxation occurring during the structuration process. In these two studies, a precise structural characterization and simple magnetoelastic models allow one to describe the magnetic behaviors of these systems.