  This article briefly reviews three topics related to the quantum critical
behavior of certain heavy-fermion systems. First, we summarize an extended
dynamical mean-field theory for the Kondo lattice, which treats on an equal
footing the quantum fluctuations associated with the Kondo and RKKY couplings.
The dynamical mean-field equations describe an effective Kondo impurity model
with an additional coupling to vector bosons. Two types of quantum phase
transition appear to be possible within this approach---the first a
conventional spin-density-wave transition, the second driven by local physics.
For the second type of transition to be realized, the effective impurity model
must have a quantum critical point exhibiting an anomalous local spin
susceptibility. In the second part of the paper, such a critical point is shown
to occur in two variants of the Kondo impurity problem. Finally, we propose an
operational test for the existence of quantum critical behavior driven by local
physics. Neutron scattering results suggest that CeCu$_{6-x}$Au$_x$ passes this
test.
