What have we learned from Dynamical Mean Field Theory and what lies ahead ?*

Dynamical Mean-Field Theory (DMFT) provides both an original perspective on the
physics of strongly correlated electron materials and an efficient computational
framework to understand and predict their properties. In this talk, I will review the
main ideas at the heart of the DMFT construction and physical perspective.
Through select examples, I will outline how the efforts of a whole community
over almost three decades have managed to develop the theory to such a point
that it can successfully be applied to a real material, taking into account its structure
and chemical composition. I will also outline how the theory is being extended
and generalized in many fruitful directions.