  This article is aimed at a pedagogical introduction to the physics of quantum
phase transitions that is unique to metallic systems. It has been recognized
for some time that quantum criticality can result in a breakdown of Landau's
Fermi liquid theory. Its converse, however, has not been appreciated until very
recently: non-Fermi liquid behavior can in turn lead to new classes of quantum
phase transition. A concrete example is provided by ``local quantum critical
points''. I summarize the theoretical reasoning and experimental evidence for
local quantum criticality, in the context of heavy fermion metals. The
underlying physics is likely to be relevant to other correlated electron
systems including doped Mott insulators.
