Electromigration is one of the most important reliability issues in semiconductor technology. Its complex character demands comprehensive physical modeling as basis for analysis. Simulation of electromigration induced interconnect failure focuses on the life-cycle of intrinsic voids, which consists of two distinct phases: void nucleation and void evolution. We present models for both phases as well as models which describe the impact of metal microstructure and mechanical stresses. These stresses have their sources in the fabrication process itself and in the material transport caused by electromigration. Special emphasis is put on explaining the void morphology and its impact on interconnect resistance. Investigations for common twoand three-dimensional interconnect structures are presented. Implications of the theoretical analysis and the simulation results for modern interconnect design are discussed.