Advances in theoretical methodologies and computational power in the last fifteen years have enabled the prediction of phonon properties with high resolution and fidelity. Notably, the use of lattice dynamics calculations, density functional theory calculations, and the Boltzmann transport equation have led to thermal conductivity predictions in agreement with experimental measurements. In this tutorial, I will describe the formulation of phonon transport modeling in bulk materials and at interfaces. A review of the underlying theory for predicting thermal conductivity and interface thermal conductance will be given first. After that, a first principles-based approach for making these predictions will be described along with examples from the literature.