  This paper discusses why the usual notion that quantum phase transitions can
be mapped onto classical phase transitions in a higher dimension, and that this
makes the former uninteresting from a fundamental theoretical point of view, is
in general misleading. It is shown that quantum phase transitions are often
qualitatively different from their classical counterparts due to (1)
long-ranged effective interactions that are induced by soft modes, and (2) in
the presence of quenched disorder, an extreme anisotropy of space-time. These
points are illustrated using various magnetic phase transitions as examples.
