In the last years the study of low-dimensional magnetic systems has become topical for its several technological applications but also for a complete understanding of the underlying physics of magnetic nanostructures. Very recently, for their challenging features, great attention has been given to the investigation of the static and dynamical properties of magnetic nanostructures. A special class of magnetic nanostructures is represented by magnonic crystals, periodic magnetic systems characterized by modulated properties. As shown by several theoretical approaches, the ferromagnetic materials composing periodic magnetic systems can be described as metamaterials whose properties arise from their structure rather than from their composition. The aim of this talk is to give an overview of the recent theoretical results obtained, via micromagnetic simulations and analytical calculations, on thin ferromagnetic films and on two-dimensional periodic systems in terms of metamaterial properties.