Known for high latent heat, small subcooling, no phase separation and low cost, organic phase change materials are widely applied in the field of phase change energy storage. However, their thermal conductivity is low. As excellent thermal conductivity enhancers, carbon-based materials boast the characteristics of high thermal conductivity, large specific surface area, light weight and strong plasticity, and can be easily processed into various shapes from one-dimensional to three-dimensional structures, with good application scenarios adaptability. Therefore, carbon-based materials are largely used in the field of phase change energy storage to enhance thermal conductivity. This article reviews the research progress on one-dimensional, two-dimensional and three-dimensional carbon-based materials modifying organic phase change materials. Among them, the three-dimensional carbon-based materials or low dimensional carbon-based materials that can be constructed into three-dimensional structures, are found to outperform comprehensively. On the one hand, the three-dimensional skeleton structure can build a continuous heat conduction path for phase change materials and improve the thermal conductivity of phase change materials. On the other hand, the porous structure of carbon-based materials can provide strong surface tension and capillary force to effectively prevent liquid phase leakage of phase change materials. Through thorough analysis, the effects of carbon-based materials on improving the thermal conductivity, liquid phase leakage and thermal properties of organic phase change materials are summarized, and the possible problems in practical application and future development direction of carbon-based materials modifying organic phase change materials are foreseen.