•PCM-cooled and PCM-heated BTMS are reviewed.•Phase change fluid (PCF), flexible phase change material (FPCM) and Hybrid cooling are analyzed.•The flammability of organic PCM needs to be solved for BTMS.•The stability of inorganic PCM needs to be solved for BTMS.•Various issues and challenges of BTMS based on PCM are identified. It is known that the performance of a power battery is greatly affected by temperature. The battery pack needs an efficient thermal management system to make the power battery work in a reasonable temperature range. Battery thermal management system (BTMs) based on phase change materials (PCM), as a passive thermal management method, has the advantages of low operating cost and good temperature uniformity. This paper mainly introduces the BTMs based on PCM, including the cooling and heating system based on PCM. For the cooling system of PCM, the performance of composite phase change materials (CPCM) and its heat transfer enhancement, phase change fluid (PCF), flexible phase change materials (FPCM), and hybrid cooling systems are analyzed. For the PCM heating system, the PCM latent heat for preheating of the power battery in a cold environment has also been discussed. Finally, this paper concluded that the next research directions should focus on the improvement of thermal conductivity of PCM, flame retardancy of organic PCM, thermal stability of inorganic PCM, PCF and FPCM, and PCM-based coupled battery thermal management.