Theories of non-Fermi liquid behavior in heavy fermions

I will review our incomplete understanding of non-Fermi liquid behavior in heavy fermion systems at a quantum critical point. General considerations suggest that critical antiferromagnetic fluctuations do not destroy the Fermi surface by scattering the heavy electrons, but by actually breaking up the internal structure of the heavy fermion. I contrast the weak, and strong-coupling view of the quantum phase transition, emphasizing puzzles and questions that recent experiments raise. (C) 1999 Elsevier Science B.V. All rights reserved.