Density Functional Theory is the method of choice for computing the electronic structure of materials. It can be used to compute the charge density, the total energy, and the atomic forces in a material system, as well as a wide variety of physical and mechanical properties.
Contrarily to more empirical or coarse grained models, DFT aims at taking into account as accurately as possible the interaction between individual electrons, at the quantum level. After briefly reviewing some applications of DFT to semiconductors and molecular devices, I will present the mathematical foundations of the theory as well as some numerical issues. I will focus in particular on the modelling of semiconductors with local defects in the framework of DFT.