Dynamical Mean Field Theory is an approach, developed in the last decade, which generalizes the cavity approach of statistical mechanics to quantum many particle systems on a lattice. Contrary to other kinds of mean field theory (e.g. Hartree) it takes into account, at least at a local level, quantum fluctuations. Since a DMFT solution for a given model can be thought as the exact solution of the model on a infinite coordination lattice its range of validity is not determined by the strength of the interactions. I will briefly review the main results of this theory. I will present our work concerning the normal and the charge ordered states in a particular lattice model. Finally I will put our findings in a general scenario for phase transitions of lattice fermions emphasizing the qualitative changes from weak to strong coupling.