For the state of the art copper dual-damascene technology, several physical mechanisms act cooperatively during void evolution under electromigration stress. Surface energy, electromigration itself, and elastic strain energy are driving forces for material transport along the void surface. Furthermore, the interaction of the void with local geometric features, such as material interfaces and microstructure, has great impact on void migration, growth, and shape stability. In particular, the high diffusivity at the copper/capping layer interface is a significant factor controlling void migration and growth along the interconnect line. However, since new materials and processes have been introduced, the adhesion between the copper and the surrounding layers has improved, resulting in grain boundary diffusion becoming more and more significant. As a consequence, a multitude of void evolution mechanisms have been observed. Current void evolution models lack appropriate description of the void development process, neglecting relevant physical phenomena that lead to interconnect failure. Moreover, these models are only suitable for simulations of simple two-dimensional interconnects and cannot realistically describe the void evolution mechanisms in modern complex interconnect structures. Therefore, they have very limited predictive capability of electromigration-induced failure development. In the scope of our work, we develop a general electromigration void evolution model. This model is the result of theoretical investigations and numerical simulations. The influence of several driving forces for atomic transport along the void surface, in connection with the local geometric properties of interconnects, has been analyzed. The model implementation in a simulation tool is followed by a careful study of the corresponding numerical algorithms. The implementation of suitable numerical methods for fully three-dimensional simulations presents a special challenge. The model implementation is validated continuously by comparison of simulation results with the available literature data and relevant experiments.