Nanostructuring materials allows independent control of multiple materials properties. High conductivity materials such as carbon nanotube forests are useful as TIMs for dissipating power in electronic devices, while low conductivity materials like nanoporous silicon for thermal barrier coatings and enhanced thermoelectric performance. Beyond thermal transport, storage of thermal energy is critical for effective heat removal for applications involving highly-transient heat fluxes, such as during operation of multiple core processors. This talk will discuss (1) methods to push the thermal conductivity to the extremes by understanding and controlling the phonon transport at the nanoscale; and (2) the development of a thermoreversible phase change material for efficient energy storage.