Emergence of two-dimensional (2D) materials with atomic-layer structures, such as graphene and MoS 2 , which have excellent physical properties, provides the opportunity of substituting silicon-based micro/nanoelectronics. An important issue before large-scale applications is the heat dissipation performance of these materials, especially when they are supported on a substrate, as in most scenarios. Thermal transport across the atomiclayer interface is essential to the heat dissipation of 2D materials due to the extremely large contact area with the substrate, when compared with their atomic-scale crosssections. Therefore, the understanding of the interfacial thermal transport is important, but the characterization is very challenging due to the limitations for temperature/thermal probing of these atomic-layer structures. In this review, widely used characterization techniques for experimental characterization as well as their results are presented. Emphasis is placed on the Raman-based technology for nm and sub-nm temperature differential characterization. Then, we present physical understanding through theoretical analysis and molecular dynamics. A few representative works about the molecular dynamics studies, including our studies on the size effect and rectification phenomenon of the graphene-Si interfaces are presented. Challenges as well as opportunities in the thermal transport study of atomic-layer structures are discussed. Though many works have been reported, there is still much room in both the development of experimental techniques as well as atomic-scale simulations for a clearer understanding of the physical fundamentals of thermal transport across the atomic-layer interfaces, considering the remarkable complexity of physical/chemical conditions at the interface.