Binary-shape memory alloys that are based on copper, mainly copper–aluminium, copper–zinc and copper–tin alloys, either with or without ternary elemental additions, are of special interest to the industry and academia because of their good shape recovery, ease of processing, larger recovery strain and lower cost. However, unlike Ni–Ti shape memory alloys, their uses are moderately limited due to shortcomings, such as stabilization of martensite due to ageing, brittleness and low mechanical strength. Therefore, efforts have been made over the years to overcome these limitations using appropriate ternary and quaternary elemental additions. This work takes into account the data obtained from the experimental work carried out by the authors of this paper as well as the data obtained from the experimental and theoretical works carried out by earlier researchers in this area that have been published in the literature over the years. It is observed in quaternary shape memory alloys based on copper that with an increase in the atomic radius of the quaternary element, the hysteresis width is found to increase. With the addition of ternary elements to binary Cu-based alloys (Cu–Al and Cu–Zn), and quaternary elements to ternary Cu-based alloys (Cu–Al–Fe, Cu–Al–Ni, Cu–Al–Mn, Cu–Zn–Al, Cu–Zn–Ni and Cu–Zn–Si), the Ms temperature either increases or decreases. This influence is directly correlated with the ev/ a ratio and cv values. It is also observed that as the concentration of electrons decreases, the Ms temperature decreases too. In addition, in this paper, we have tried to obtain relationships between the Ms temperature and the mass or atomic% of different elements through multiple regressions to generalize the interpretations. © 2019, Indian Academy of Sciences.