Energy transport at the nanoscale differs fundamentally from that at the bulk scale. Characterization and understanding of the unique energy transport phenomena that arise at the nanoscale is key to developing novel technological applications such as energy conversion devices and atomic-scale device components. In this talk, I will present my work on understanding unique thermal transport in various nanomaterials. I will also discuss heat dissipation in atomic-scale junctions that are composed of single atomic chains or single molecules. Further, experimental techniques to perform challenging experiments will be briefly described.