Colloquium: Antonio Garcia-Garcia Princeton University Department of Physics Title: Anderson localization: fifty years old and still growing. Abstract: The phenomenon of Anderson localization is object of renewed interest mainly due to two recent developments: the experimental realization of disorder in ultra cold atoms (and also light) and the progress in numerical simulations. Firstly I give a brief overview of the field with a special emphasis on the physics of the metal-insulator transition. Then I describe the main advances of the last few years and the challenges for the future. In the second part I summarize my recent research on this topic: 1. The introduction of an analytical theory of the metal-insulator transition that provides explicit expressions of typical quantities characterizing the transition, such as critical exponents or level statistics. 2. The proposal of a theoretical framework to describe localization in quantum chaos, namely, quantum systems whose classical counterpart is deterministic but chaotic. In particular I identify in what situations a metal insulator transition is expected in quantum chaos. In low (d<2) dimensions it is shown to be characterized by a certain type of classical superdiffusion. The example of a kicked rotor with classical singularities, relevant for experiments with cold atoms, is discussed in detail.