Of particular interest for thermal management of electronic and photonic devices is the ability to tune and direct heat transfer within systems as they continue to shrink. For materials where phonons are the dominant thermal energy carriers, nanostructuring enables tuning of the thermal properties during fabrication. For example, strategically-engineered periodically porous materials can create bandgaps in the phonon dispersion relationship. Furthermore, strain can impact the atomic vibrations and the interaction of the nanostructuring and the applied strain could be used to control thermal transport performance. Strategic design of the nanostructure relative to the applied strain can actively enhance or reduce the anisotropy in in-plane thermal conductivity of such structures. This talk will focus on methods to tune the thermal conductivity of nanostructured materials by understanding and controlling the phonon transport at the nanoscale including both tuning of properties during fabrication and active tuning of properties with strain.