Quantum Simulators.

According to Feynman the best way to simulate a complex quantum system is to use another quantum system. When realised, a quantum simulator might become an amazingly efficient tool to study a variety quantum many-body systems. After so many years from Feynman's proposal the level of experimental control on certain quantum many-body systems became such that Feynman's vision has become reality. At present there is a number of platforms, ranging from cold atoms in optical lattices to trapped ions and solid state nano-circuits that are best suited to this aim. Together with the impressive progresses in the new emerging quantum technologies, a large body of theoretical work has shaped and widen considerably the field of quantum simulations. Numerous experimental and theoretical works found applications of quantum simulators in a wide range of fields from condensed-matter physics to high-energy physics, from quantum chemistry to cosmology. In my presentation I will give a general overview of the present activity in this field. I will highlight some of the potentialities of quantum simulators and will look as well into the future with a discussion of some open problems.