Heat conduction is of both fundamental and applied interests. Phonon mediated lattice thermal conduction is the domin-ant mechanism for heat conduction inside an optically opaque and electrically insulating solid. Despite rapid developme-nts in computational materials physics, accurate prediction of lattice thermal conductivity of solids, especially those wi-th complex structures and/or compositions, remains a challenge. In this talk, I will present our recent work on first principles calculations of lattice thermal conduction of crystalline materials. Our method combines the first-principles total energy theory, quantum scattering theory, and kinetic Peierls-Boltzmann transport theory. We have successfully adopted this technique to predict the lattice thermal conductivity of (1) Earth's lower mantle minerals (MgO and MgSiO3 Perovskite) at extreme pressure an temperature conditions, and (2) thermoelectric materials PbTe.