Thermal transport in semiconductors is dominated by phonons, quanta of energy associated with atomic vibrations. Advances in computational techniques and power have made it possible to predict the frequencies, group velocities, and lifetimes of individual phonon modes from density functional theory calculations. From these properties, a bottom-up understanding of thermal conductivity can be developed. In this seminar, I will outline the procedure for calculating phonon properties and thermal conductivity and then describe three recent studies from my group : A demonstration of how strain affects phonon properties and thermal conductivity differently in soft and stiff materials, A prediction of strongly-anisotropic thermal conductivity in single-layer black phosphorene, and The separation of the phonon and electron contributions to the thermal conductivity of metals.