Theoretical study of mineral physics has rapidly progressed by first principles method based on the density functional theory. In this article, recent studies of the Earth's constituents and related materials by means of the first principles electronic structure calculation methods are reviewed. Especially, calculations of high-pressure thermodynamic properties, PVT equations of state, high-pressure elasticity, high-PT phase stability are reported. These techniques are applied to study thermochemical state and physical properties of the Earth's lower mantle.