High entropy shape memory alloy ia a novel type of high temperature shape memory alloy developed on the basis of NiTi alloy with equal atomic ratio and the concept of high entropy alloy. In recent years, the (TiZrHf)₅₀(NiCoCu)₅₀ and (TiZrHf)₅₀(NiCuPd)₅₀ series high entropy shape memory alloys with excellent comprehensive properties have been developed, which has attracted extensive attention and research interest. In this paper, the research progress of high entropy shape memory alloy is reviewed from the aspects of phase composition, microstructure, martensitic phase transformation behavior, shape memory effect and superelasticity. Simultaneously, the future inveatigate keynote of high entropy shape memory alloy is also prospected.