The two-dimensional (2D) materials represented by graphene and boron nitride provide an excellent platform for the study of thermal conduction and the interfacial thermal resistance in low-dimensional system. Recent studies recover exotic physics behind the novel thermal transport properties of 2D materials, such as length effect, dimensional effect, isotopic effect, anisotropic effect, etc. In this review, we introduce the recent progress of thermal properties in 2D materials in the last decade. The principle and development of thermal conduction measurement technologies used in 2D materials are introduced, followed by the experimental progress of thermal conduction and interfacial thermal resistance. Special attention is paid to the abnormal thermal transport and relevant physical problems. Finally, we present thermal management and heat dissipation in 2D electronic devices, summarize and point out the problems and bottlenecks, and forecast the future research directions and foregrounds.