Abstract: Graphene has attracted much attention due to its unique structure and excellent thermal conductivity, which is widely used in energy materials, battery materials, thermal composite materials fields as a two-dimensional material with high thermal conductivity. It is of great significance to deepen the understanding of solid-state heat transfer mechanisms by theoretical and experimental research on the thermal conductivity of graphene, and it can guide the design of the development of energy technology, thermal management and heat dissipation technology of electronic devices and the high-efficiency thermal conductivity materials. In recent years, there are numerous reports on the thermal conductivity of graphene, and it is beneficial for researchers to carry out their work more effectively by summarizing these reports on the thermal conductivity of graphene. This work summarizes the testing methods, influencing factors, and application status of the thermal conductivity of graphene. Firstly, the thermal conductivity measurement methods of single-layer, few-layer and multilayer graphene and graphene matrix composites are introduced, including Raman spectroscopy, thermal bridge, laser flash and 3ω method. Then, the theoretical research achievements on the thermal conductivity of graphene was summarized and the influence factors of the intrinsic thermal conductivity of graphene such as size, number of layers and defects were discussed. Next, the application of graphene as a thermal conductor in energy materials, battery materials and modified composite materials is summarized. Finally, the research on graphene's thermal conductivity is concluded and the current challenges and issues was highlighted in graphene's thermal conductivity research. Moreover, the prospect for future development direction is proposed.