Recent works have demonstrated that the thermal phonons responsible for heat conduction possess a broad spectrum,yet this spectrum remains unknown for most materials and is not always accounted for in simulations due to computational cost.In this talk,I will describe our efforts to directly measure and engineer the thermal phonon spectrum using computation and experiment.Experimentally,I will describe our efforts to provide a rigorous interpretation of quasiballistic thermal transport in mean free path spectroscopy.Computationally,I will demonstrate the importance of considering the size distribution of nanostructures to achieve the minimum thermal conductivity in solids.