Band ferromagnetism versus collective Kondo state in lattice fermion models

It is becoming widely recognized that, contrary to earlier expectations, the usual one-band Hubbard model does not give an explanation for itinerant ferromagnetism. After reviewing the status of magnetic ordering in the one-band model, we discuss the possibility of ferromagnetism in some recently introduced two-band Hubbard models, and in generalized Anderson lattices. It is argued that these two classes of models are closely related and that it is their common feature that the ferromagnetic phase has to compete with a collective Kondo state.