Breakdown of the Fermi liquid theory in heavy fermion compounds

We review the anomalous properties of heavy fermion compounds like CeCu$_{6-x}$Au$_x$ or CeMIn$_5$ close to a zero temperature phase transition called a quantum critical point. Anomalous behavior of the resistivity, specific heat and magnetic properties observed in various compounds suggests a fundamental breakdown of the Fermi liquid theory. Recent measurements on YbRh$_2$Si$_2$, field-tuned through the quantum critical point, provide interesting insights on the evolution of the Fermi liquid close to criticality. We discuss the possibility of a kind of spin-charge separation at the quantum critical point and make some remarks about its possible link with the underscreened Kondo model.