  A quantum system can undergo a continuous phase transition at the absolute
zero of temperature as some parameter entering its Hamiltonian is varied. These
transitions are particularly interesting for, in contrast to their classical
finite temperature counterparts, their dynamic and static critical behaviors
are intimately intertwined. We show that considerable insight is gained by
considering the path integral description of the quantum statistical mechanics
of such systems, which takes the form of the {\em classical} statistical
mechanics of a system in which time appears as an extra dimension. In
particular, this allows the deduction of scaling forms for the finite
temperature behavior, which turns out to be described by the theory of finite
size scaling. It also leads naturally to the notion of a temperature-dependent
dephasing length that governs the crossover between quantum and classical
fluctuations. We illustrate these ideas using Josephson junction arrays and
with a set of recent experiments on phase transitions in systems exhibiting the
quantum Hall effect.
