While the classical modelling and analysis approach is efficient for systems evolving on Euclidean spaces or manifolds, many recent applications require the development of mathematical tools for state spaces with a more complicated structure, such as a fractal, a stratified set or a topological graph or, in the case of many interacting evolutions, for a collection of different state spaces. These special structures arise naturally in a number of applied problems ranging from mechanical ones as for the static and dynamics of granular media to biological ones as vessels pattern formation in angiogenesis. Such problems can be studied by developing an analysis directly on the complicated media or via limiting procedures on the microstructure to obtain auxiliary systems on classical spaces, with the appearance of new terms in classical equations and/or enlarged state spaces. This situation is typical of discrete networks, which can be used to approximate hard problems on continua, or can be studied by continuum limits. Also, an example of limiting procedure is given by homogenization limits for various materials with several constituents. Other important examples include continuum networks, i.e. one dimensional complexes, which are the natural space for car traffic or telecommunication data flow. The determination of the natural dynamics or the typical stochastic behavior at vertices requires an investigation of flows in networks. The presence of different time or space scales may give rise to similar phenomena requiring singular perturbation methods, mean fields analysis and other limiting procedures.