Superconductivity in the iron pnictides and chalcogenides arises at the
border of antiferromagnetism, which raises the question of the role of quantum
criticality. In this topical review, we describe the theoretical work that led
to the prediction for a magnetic quantum critical point arising out of a
competition between electronic localization and itinerancy, and the proposal
for accessing it by using isoelectronic P substitution for As in the undoped
iron pnictides. We go on to compile the emerging experimental evidence in
support of the existence of such a quantum critical point in
isoelectronically-tuned iron pnictides. We close by discussing the implications
of these results for the physics of the iron pnictides and chalcogenides.Comment: 20 pages, 9 figure