High-entropy shape-memory alloys (HESMAs) exhibit unique properties, including high yield strength, a wide temperature range of phase transformation, and excellent thermal cycling stability, among others. Hence, they have broad prospects for research and application. Currently, various new high-entropy shape-memory alloys have been developed based on TiNi, Fe-based, Ti-based, and NiMn-based alloys. This article focuses on summarizing and analyzing the research status of various types of high-entropy shape-memory alloys, including their microstructure characteristics, martensitic phase transformation, and functional properties. The advantages and disadvantages of high-entropy shape-memory alloys compared to traditional shape-memory alloys are briefly discussed. Finally, based on the analysis of existing problems, future research prospects are proposed, hoping to provide assistance for the development and application of high-entropy shape-memory alloys in the future.