Study of diffusion in multilayers is very important for better understanding of their thermal stability. Furthermore, since in these systems the characteristic distance of diffusion is typically few nanometers, the investigation of diffusion leads to an improvement of our knowledge on effects more expressed on this length scale (gradient energy, stress effects, non-linearities). In this review results on finite difference simulations of the interplay of stresses and non-linearities (caused by the strong concentration dependence of the diffusion coefficient) will be summarised for bulk interdiffusion in binary systems with mutual solubility. On the other hand possible failure mechanisms for multilayers of non-reactive immiscible materials will be reviewed. It will be illustrated that in these cases the interface and grain-boundary assisted mechanisms (pinhole formation at triple junctions and material transport along interfaces and grain-boundaries) offer the most effective way of destratification. The role of stresses in these processes will be also discussed. Finally it will be shown that at low temperatures (where the bulk diffusion is frozen) a similar mechanism can lead to the beak-up of the structure in completely soluble systems as well.