  Strongly correlated electron systems at the border of magnetism are of active
current interest, particularly because the accompanying quantum criticality
provides a route towards both strange-metal non-Fermi liquid behavior and
unconventional superconductivity. Among the many important questions is whether
the magnetism acts simply as a source of fluctuations in the textbook Landau
framework, or instead serves as a proxy for some unexpected new physics. We put
into this general context the recent developments on quantum phase transitions
in antiferromagnetic heavy fermion metals. Among these are the extensive recent
theoretical and experimental studies on the physics of Kondo destruction in a
class of beyond-Landau quantum critical points. Also discussed are the
theoretical basis for a global phase diagram of antiferromagnetic heavy fermion
metals, and the recent surge of materials suitable for studying this phase
diagram. Furthermore, we address the generalization of this global phase
diagram to the case of Kondo insulators, and consider the future prospect to
study the interplay among Kondo coherence, magnetism and topological states.
Finally, we touch upon related issues beyond the antiferromagnetic settings,
arising in mixed valent, ferromagnetic, quadrupolar, or spin glass f-electron
systems, as well as some general issues on emergent phases near quantum
critical points.
