Quantum criticality describes the collective fluctuations of matter undergoing a second‐order phase transition at zero temperature. It is being discussed in a number of strongly correlated electron systems. A prototype case occurs in the heavy fermion metals, in which antiferromagnetic quantum critical points (QCPs) have been explicitly observed. Here, I address two types of antiferromagnetic QCPs. In addition to the standard description based on the fluctuations of the antiferromagnetic order, a local QCP is also considered. It contains inherently quantum modes that are associated with a critical breakdown of the Kondo effect. Across such a QCP, there is a sudden collapse of a large Fermi surface to a small one. I also consider the proximate antiferromagnetic and paramagnetic phases, and these considerations lead to a global phase diagram. Finally, I discuss the pertinent experiments and outline some directions for future studies.