Failure mechanisms in materials and structures can be studied on different length scales. On a structural level, failure can be observed as the propagation of a single crack. However, when zooming into the apparent crack tip, it is revealed that the actual failure process is set by the nucleation and growth of multiple micro-cracks that together form the dominant crack. In crystalline materials, the nucleation of cracks can be traced back to even smaller levels of observation. The collective glide of dislocations in the atomistic structure of these materials appears to be the driving mechanism for the nucleation of micro-cracks near free edges. From a mathematical point of view the creation and propagation of cracks and the glide of dislocations can be considered as evolving discontinuities in the material. This thesis focuses on the numerical representation of these discontinuities on different length scales, varying from the simulation of delamination growth in fibre-metal laminates to a model that incorporates slip due to the motion of discrete dislocations.