Abstract: Magnetic nanostructures have received a lot of attention in latest years, both from a fundamental point of view and for several potential technological applications. In the last few years, these structures have become one of the most important and exciting areas of solid state research. One very interesting field of magnetism is the study of the spin dynamics. Collective excitation of microscopic magnetizations are called spin waves. In the last years, spin waves have been widely investigated both from the theoretical and experimental point of view in thin films, in isolated elements. Recently, it has also been found that periodic systems can support the propagation of collective spin waves. Such systems are called magnonic crystals and they open a new possibility to tailor the dynamic properties at the nanoscale, e.g. by modifying band structures through patterning. A prominent application that will be discussed in this presentation are frequency filters.