The purpose of this work is to establish the notion of process signatures in the context of manufacture processing. In this context we provide an overview of selected computational approaches which are capable of resolving the basic features of non-linear heterogeneous microstructures and process related boundary and loading conditions. As an example, the cohesize zone element method is employed to predict the state of damage and fracture in coated systems. The latter are composed of CrN-or AlN-based protective coating layers and steel-based substrates. The state of damage and fracture is simulated for nano-indentation tests and discussed at different deformation stages. Furthermore, the influence of residual stresses within the polygrain microstructure on the evolution of damage and fracture is analyzed. Lastly, future developments and computational challenges are discussed.