• Preparation methods of FPCMs are reviewed and compared. • Properties of FPCMs are summarized and analyzed. • Applications of FPCMs are introduced in detail. • Various issues and challenges of FPCMs are identified. Phase change materials (PCMs) have been widely used in various fields of thermal energy storage because of their large latent heat value and excellent temperature control performance. Based on the microstructure packaging strategy, PCMs are developed into shape-stabilized PCMs, which can solve the problem of leakage when phase change occurs. However, shape-stabilized PCMs usually have the disadvantage of poor mechanical properties, and the thermal resistance increases due to the poor fit with heat transfer elements. With the development of flexible electronic devices and wearable devices, flexible phase change materials (FPCMs) with excellent mechanical properties have become a hot spot. This paper introduces the preparation methods of FPCMs from both internal molecular support and external skeleton support. In addition, the flexibility mechanism and the properties of FPCM are summarized and analyzed. Furthermore, the potential applications of FPCMs in thermal management of electronic devices, wearable devices and others are presented in detail. Finally, the main problems, solutions and future directions are put forward and discussed.