Density functional theory of the electronic structure of condensed matter is reviewed with an emphasis on its application to geophysics. The review is placed within the context of our attempts to understand planetary interiors and the unique features of these regions that lead us to use band-structure theory. The foundations of density functional theory are briefly discussed, as are its scope and limitations. Special attention is paid to commonly used approximations of the theory, including those of the exchange-correlation potential and the structure of the electronic core. Some of the important computational methods are reviewed, including the linearized augmented plane-wave method and the plane-wave pseudopotential method. Examples of applications of density functional theory to the study of the equation of state, crystalline structure, phase stability, and elasticity of earth materials are described. Some critical areas for further development are identified.