  The identification of magnetic quantum critical points in heavy fermion
metals has provided an ideal setting for experimentally studying quantum
criticality. Motivated by these experiments, considerable theoretical efforts
have recently been devoted to reexamine the interplay between Kondo screening
and magnetic interactions in Kondo lattice systems. A local quantum critical
picture has emerged, in which magnetic interactions suppress Kondo screening
precisely at the magnetic quantum critical point (QCP). The Fermi surface
undergoes a large reconstruction across the QCP and the coherence scale of the
Kondo lattice vanishes at the QCP. The dynamical spin susceptibility exhibits
$\omega/T$ scaling and non-trivial exponents describe the temperature and
frequency dependence of various physical quantities. These properties are to be
contrasted with the conventional spin-density-wave (SDW) picture, in which the
Kondo screening is not suppressed at the QCP and the Fermi surface evolves
smoothly across the phase transition. In this article we discuss recent
microscopic studies of Kondo lattices within an extended dynamical mean field
theory (EDMFT). We summarize the earlier work based on an analytical
$\epsilon$-expansion renormalization group method, and expand on the more
recent numerical results. We also discuss the issues that have been raised
concerning the magnetic phase diagram. We show that the zero-temperature
magnetic transition is second order when double counting of the RKKY
interactions is avoided in EDMFT.
