Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Psi(r(1),r(2),r(3),...). Having been widely used for over 30 years by physicists working an the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications : the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.