How do Fermi liquids get heavy and die?

We discuss non-Fermi liquid and quantum critical behaviour in heavy-fermion materials, focusing on the mechanism by which the electron mass appears to diverge at the quantum critical point. We ask whether the basic mechanism for the transformation involves electron diffraction off a quantum critical spin-density wave, or whether a breakdown in the composite nature of the heavy electron takes place at the quantum critical point. We show that the Hall constant changes continuously in the first scenario, but may `jump' discontinuously at a quantum critical point where the composite character of the electron quasiparticles changes.