  The standard description of quantum critical points takes into account only
fluctuations of the order parameter, and treats quantum fluctuations as extra
dimensions of classical fluctuations. This picture can break down in a
qualitative fashion in quantum critical metals: non-Fermi liquid electronic
excitations are formed precisely at the quantum critical point and appear as a
part of the quantum-critical spectrum. In the case of heavy fermion metals, it
has been proposed that the non-Fermi liquid behavior is characterized by the
destruction of the Kondo effect. The latter invalidates Hertz's Gaussian theory
of paramagnons and leads to an interacting theory that is ``locally quantum
critical''. We summarize the theoretical and experimental developments on the
subject. We also discuss their broader implications, and make contact with
recent work on quantum critical magnets.
