  Zero temperature phase transitions not only occur in the bulk of quantum
systems, but also at boundaries or impurities. We review recent work on quantum
phase transitions in impurity models that are generalizations of the standard
Kondo model describing the interaction of a localized magnetic moment with a
metallic fermionic host. Whereas in the standard case the moment is screened
for any antiferromagnetic Kondo coupling as T to 0, the common feature of all
systems considered here is that Kondo screening is suppressed due to the
competition with other processes. This competition can generate unstable fixed
points associated with phase transitions, where the impurity properties undergo
qualitative changes. In particular, we discuss the coupling to both non-trivial
fermionic and bosonic baths as well as two-impurity models, and make
connections to recent experiments.
