Energy storage technology can solve the contradiction between energy supply and demand in time and space and thus improve energy utilization efficiency. As a potential heat storage technology,phase change heat storage is widely used in solar energy,energysaving buildings,industrial waste heat recovery and thermal management systems. Its heat storage medium is phase change materials(PCMs) which mainly include solidsolid PCMs and solidliquid PCMs. The PCMs can achieve the dual purposes of heat storage and temperature control due to their large latent heat and constant phase change temperature. Solidliquid PCMs are a kind of phase change materials that are widely studied. They have the advantages of highenergy storage density,adjustable phase change temperature,stable chemical properties and low price. However,the application of solidliquid PCMs is hindered by liquid leakage during phase change,low thermal conductivity and phase separation. Those problems can be solved by introducing porous materials into solidliquid PCMs. Particularly,the shapestabilized PCMs prepared with porous carbon matrix exhibit enhanced mechanical strength,improved thermal conductivity,excellent encapsulation and stability. This review systematically summarizes the research progress of porous carbonbased shapestabilized PCMs. The effects of the pore structure,surface modification,mass fraction and intermolecular force of expanded graphite,carbon nanotubes,graphene oxides and biological porous carbon on the shapestabilized capacity,thermal performances and phase change behaviors of shapestabilized PCMs are analyzed. Meanwhile,the performances of shapestabilized PCMs prepared with other porous carbon matrices are discussed,such as active carbon,carbon foam and carbon nitride. The research status on the application of porous carbonbased shapestabilized PCMs is also introduced. At last,by comparing the main performances and different advantages of shapestabilized PCMs prepared with different porous carbon matrix,some suggestions for material selection in the application are put forward. Also,the future research topics are outlined