Novel experimental possibilities together with improvements in computer hardware as well as new concepts in computational mathematics and mechanics – in particular multiscale methods – are now, in principle, making it possible to derive and compute phenomena and material parameters at a macroscopic level from processes that take place one to several scales below. Because of this quest to analyse and quantify material behaviour at ever lower scales, more often (evolving) discontinuities have to be taken into account explicitly. Also, many applications require that one or more diffusion-like phenomena are considered in addition to a standard stress analysis. Accordingly, multiscale analysis, multi-physics and the ability to explicitly and accurately model evolving discontinuities are important challenges in computational science, and further progress on these topics is indispensible for an improved understanding of the behaviour and properties of materials. In this contribution we will give an impression of some developments.