Nanostructuring leads to unique material properties and combinations of properties not typically found in bulk materials. Of particular interest is the ability to tune the thermal transport properties through nanostructuring yielding high conductivity materials such as carbon nanotube forests for dissipating power in electronic devices and low conductivity materials like porous silicon for thermal barrier coatings and enhanced thermoelectric performance. This Technology/Science Update Talk will focus on methods to push the thermal conductivity of nanostructured materials to the extremes by understanding and controlling the phonon transport at the nanoscale.