Bose-Einstein condensates in optical potentials

One of the most fascinating frontiers of modern physics is the possibility to use laser light to manipulate the motion of atomic samples. In the last two decades, spectacular advances in laser cooling techniques have made the production of Bose-Einstein condensates of neutral atoms possible. These quantum objects, nowadays routinely produced in many laboratories all over the world, are invaluable tools for the study of fundamental problems of quantum mechanics on a macroscopic scale. The possibility to use far-detuned laser light to engineer specific kinds of potentials allows an unprecedented control of the forces exerted on a quantum system. In this review we present an introduction to the physics of Bose-Einstein condensates in optical potentials. The main body of the paper is focused on Bose-Einstein condensates in optical lattices, i.e. periodic potentials created with laser light standing waves. These systems have allowed the investigation of many fundamental problems of physics, throwing a bridge between the realm of atomic physics and the one of solid state physics. Furthermore, they represent promising resources for studies in the field of many-body quantum correlated systems, also in the perspective of applications in the field of quantum computation. Finally, we consider the possibility of producing disordered potentials with light, as realized in recent experiments aiming at the study of the emergence of disorder-induced localization effects