Carbon nanotubes (CNTs), as potent reinforcements in composites, have demonstrated excellent strengthening effects when combined with copper in numerous recent studies. Challenges remain in the application of these composites and in fully leveraging the reinforcing capabilities of CNTs to achieve comprehensive performance enhancement. The performance of CNTs/Cu composites can be flexibly regulated owing to the unique structure and properties of CNTs. To achieve the fabrication of high-performance and diverse CNTs/Cu composites, a profound understanding of the reinforcement mechanisms of CNTs in the composites is essential, along with the consideration of key influencing factors on performance. This article provides a comprehensive overview of the reinforcement mechanisms of CNTs on the mechanical, electrical, and thermal properties of CNTs/Cu composites. Factors influencing the effectiveness of CNT reinforcement in composites are discussed, including the attributes and dispersion of CNTs, the architectures of composites, and the interface between CNTs and Cu. Furthermore, this study explores the role of CNTs in addressing the trade-off between high strength and high conductivity as well as between high strength and high ductility in the copper matrix.