We present a theoretical analysis based on self-consistent numerical simulations of current-driven interactions between voids in metallic thin-film interconnects and the resulting void migration, morphological evolution, and coalescence phenomena. The analysis reveals the complex nature of electromigration-induced void-void interactions, and their implications for the evolution of interconnect line electrical resistance. Most importantly, it is demonstrated that current-driven void-void interaction effects, such as void coalescence, can cause sudden changes in the interconnect line electrical resistance, in qualitative agreement with observations in accelerated electromigration testing experiments.