As component dimensions in integrated circuits shrink to extreme scales, the complexity of interconnect systems is skyrocketing, necessitating an urgent and comprehensive upgrade of interconnect materials and manufacturing processes. As the “bridge” linking various on-chip components, the performance of interconnect materials directly influences overall chip performance, and their evolution has long been a critical driver of advances in chip technology. In recent years, copper-carbon nanotube (Cu-CNT) interconnects have garnered significant attention for offering electrical conductivity that surpasses pure copper alongside a more straightforward fabrication process. Despite the exceptional overall performance of Cu-CNT composites, systematically elucidating their bulk behavior and interfacial bonding mechanisms remains a formidable challenge. Overcoming this bottleneck requires in-depth investigation of the complex interactions at the Cu-CNT interface and assessment of their effects on the material’s mechanical stability and thermal management performance. This review summarizes the applications of atomic-scale first-principles calculations, molecular dynamics simulations, multiphysics modeling, and machine learning methods to Cu-CNT materials and illustrates their use with examples from representative and recent studies. Specifically, it emphasizes the pivotal role of machine learning in deciphering the mechanisms of Cu-CNT composites across multiple spatial and temporal scales. This review not only provides a systematic reference for academic research and engineering applications of Cu-CNT-based chip interconnect materials, but also offers perspectives for the development of next-generation high-performance interconnects.