Density Functional Theory (DFT) has become a major tool in chemistry, materials science, molecular biology and nanotechnology. It is also an inexhaustible source of exciting mathematical and numerical issues. In this talk, I will present some of the variational models derived from DFT, and discuss their mathematical properties. I will focus in particular on the modeling of crystals with local defects. I will show that local defects are always neutral in the Thomas-Fermi-von Weizsäcker (TFW) theory of crystals. In this respect, all crystals therefore behave as metals. The situation is more complex for the Hartree model, which is able to describe not only metals, but also insulators and semi-conductors. In the latter cases, two different values for the charge of a local defect are obtained, depending on the viewpoint adopted. The first value corresponds to the bare charge, the second one to the screened (or renormalized) charge. The fact that these two values differ is a consequence of the long-range of the Coulomb potential.