Abstract: Heat dissipation in micro-nano-scale devices is one of the bottlenecks which hinder the further development of the semiconductor industry. A series of procedures should be performed to dissipate the heat generated by the electronic device to the environment, which involves the thermal transport across interfaces and high performance heat conducting materials. We first review the recent progress in the field of micro-nano-scale thermal transport in solids from both the theoretical and experimental approaches. In the area of thermal transport theory and computational methodology, the Boltzmann transport equation, molecular-dynamics simulation, and Green’s function are discussed. For the thermal transport experiments, we present an introduction to scanning thermal microscopy which is used to measure the spatial temperature distribution of sample surfaces, as well as the ultra-fast thermoreflectance technique which is used to measure the thermal conductivity of thin films and thermal boundary resistance. Then we tackle the problem of heat transport across an interface, including the calculation of thermal boundary resistance and how this is affected by the electron-phonon interaction. Several new heat conducting materials are also discussed, including carbon-based materials, boron-nitride whose crystal structure is similar to that of graphene, polymer chains, and thermal interface materials.