  Quantum phase transitions arise in many-body systems due to competing
interactions that promote rivaling ground states. Recent years have seen the
identification of continuous quantum phase transitions, or quantum critical
points, in a host of antiferromagnetic heavy-fermion compounds. Studies of the
interplay between the various effects have revealed new classes of quantum
critical points, and are uncovering a plethora of new quantum phases. At the
same time, quantum criticality has provided fresh insights into the electronic,
magnetic, and superconducting properties of the heavy-fermion metals. We review
these developments, discuss the open issues, and outline some directions for
future research.
