Towards a Theory of Strongly Correlated Materials the Dynamical Mean Field Theory Road

Strongly corrrelated electron materials, pose great conceptual and computational challenges. Dynamical Mean Field Theory (DMFT) has enabled a community of scientists to achieve great progress in this area. We will review some basic ideas underlying this approach, such as the reduction of the full many body problem into a quantum impurity model satisfying a self consistency condition. We will then provide some examples from materials containing elements from different regions of the periodic table, ranging from 3d's(*) to 5f's (**) of how DMFT ideas and implementations in combination with electronic structure methods has enabled predictions in materials which were not tractable by other methods, work under way to overcome its limitations(*) and point towards great challenges ahead.