Shape memory alloys (SMAs) are ones which can return to their original shape under impact of temperature or external magnetic field. The SMAs are capable of many applications in the fields of biomedical, aerospace, microelectronics, automation, for examples, orthodontics, stents, bone anchors, automatic valves, heat sensors, nanotweezers, robots... Recently, researchers have discovered the shape memory effect (SME) on high entropy alloys (HEAs). The combination of superior properties of SMAs and HEAs (high strength, heat resistance, low diffusion coefficient...) would bring useful practical applications in practice. In this paper, we will present an overview of the research situation of SMAs and our initial results obtained on Ni-Ti based alloys of Ni-Ti, Ni-Ti-Zr-Cu-Cr, Ni-Ti-Zr-Cu-Co, Ni-Ti-Zr-Cu-Nb, and Ni-Ti-Zr-Cu-Hf prepared by melt-spinning method.