The standard model of solids, grounded on Fermi Liquid theory and powerful computational techniques, provides an accurate description of many materials of great technological significance. Correlated electron systems are materials which fall outside the standard model of solid state physics. They display remarkable emergent phenomena as for example metal to insulator transitions and unconventional high temperature superconductivity. The most recent example provided by the iron based high temperature superconductors. From a theoretical perspective correlated electrons pose a most challenging non-perturbative problem in physics. In this colloquium I will give an elementary introduction to the field of strongly correlated electron systems and Dynamical Mean Field Theory (DMFT) a non perturbative method which provided a zeroth order picture of the strong correlation phenomena in close analogy with the Weiss mean field theory in statistical mechanics. Applications to materials containing f and d electrons will be presented to show how the anomalous properties of correlated materials emerge from their atomic constituents. Different roads for the formation of strongly correlated states, will be traced to Mott Hubbard and Hunds physics. I will conclude with an outlook of the challenges ahead and the perspectives for rational material design using strongly correlated materials. |