Broad-based interest in microscale heat transport, engineered phononic materials, metamaterials, and their relevant systems has created significant demand for computational approaches to aid in investigation and design of materials that support phonons. Mainstay approaches such as molecular dynamics, lattice dynamics, and Boltzmann Transport equation continue to advance the field often being extended to the limits of their physical or numerical validity. New materials beyond traditional group-IV, III-V, and II-VI semiconductors, phenomena that critically depend on scattering, low-dimensional nanostructures, high temperature applications, and roles played by defects continue to push these limits. In this talk, we will describe recent efforts to consider the challenges of phonon manipulation in materials that have unprecedented levels of microstructure and lattice complexity. Specifically, we will describe computational developments to investigate phonon transport in nitramine molecular crystals, 2D materials experiencing extreme deformation, and delocalized phonon effects due to complex lattice defects.