The electromigration behavior of copper interconnects realized in dual damascene architecture indicates that a microstructure of copper plays a significant part in the failure development. A characteristic effect of the microstructure on electromigration-induced void nucleation is the placement of such a void at triple point sites of the grain boundary network. Contemporary process techniques aimed at strengthening the copper/capping and copper/barrier layer interfaces eliminate to a large extent the menace of typical electromigration paths along copper interfaces to surrounding layers but increase the effect of grain boundary networks as well as crystal orientations inside the grains. Thermal or electromigration induced mechanical stress represents a further complication, as it not only serves as an additional driving force for the material transport but also causes anisotropy of the common self-diffusion process which accompanies electromigration. Such connections among electromigration, copper microstructure, and mechanical stress pose two main problems for the modern interconnect reliability TCAD. First, electromigration simulation must encompass the effect of the fast diffusivity paths along the grain boundaries and the effect of mechanical stress on the diffusion mechanisms in these paths. The development of simulation tools must be preceded by a comprehensive theoretical analysis of the diffusion processes at the atomic level. This theoretical analysis is supported by density functional theory (DFT), molecular dynamics (MD), and Kinetic Monte Carlo (KMC) simulations. The electromigration simulation tool itself is based on the macroscopic continuum models, but these models are built, modified, and parameterized on the basis of theoretical analysis and microscopic (DFT, MD, KMC) simulations. Second, the microstructure of copper is a function of dual damascene process parameters. Electroplating has shown superior ability to fill submicron trenches and vias of dual damascene architectures. In the hours after electroplating, copper microstructure undergoes significant transformations, as result of which micro-stresses develop. Connecting of parameters of the electroplating process to the grains' shape and size and the crystal orientation inside the grains is the major issue for the theoretical analysis. Relying on the understanding of physical phenomena, advanced numerical methods, such as multi-level set and high order finite elements, are utilized to simulate copper microstructure evolution together with dynamics of microstructural stresses. For the simulation of the general stress development caused by thermal mismatch and microstructural evolution, finite element based, multi-physics simulation tool StrDep has been developed. This tool has already been successfully applied in the scope of the European Union PROMENADE project.