Cu-based shape memory alloys (SMAs) and among these copper–zinc (Cu–Zn), copper–aluminum (Cu–Al), and copper–tin (Cu–Sn) alloys both with and without ternary additions have shown potential due to their good shape recovery, ease of fabrication, excellent conductivity of heat and electricity. However, their applications are still limited because of the shortcomings of thermal stability, brittleness, and mechanical strength, which are closely related with microstructural characteristic of Cu-based SMAs, such as coarse grain sizes, high elastic anisotropies, and the congregation of secondary phases or impurities along the grain boundaries. Efforts are being made to overcome these drawbacks with proper ternary additions, adopting alternative processing routes and also optimizing the heat treatment cycles. The present article will deal with the current status of research and commercialization of Cu-based SMAs and dwell upon the future directions in which research should be targeted and future prospects of converting the research into components for commercial use.