  The Chiral Magnetic Effect (CME) is the phenomenon of electric charge
separation along the external magnetic field that is induced by the chirality
imbalance. The CME is a macroscopic quantum effect - it is a manifestation of
the chiral anomaly creating a collective motion in Dirac sea. Because the
chirality imbalance is related to the global topology of gauge fields, the CME
current is topologically protected and hence non-dissipative even in the
presence of strong interactions. As a result, the CME and related quantum
phenomena affect the hydrodynamical and transport behavior of systems
possessing chiral fermions, from the quark-gluon plasma to chiral materials.
The goal of the present review is to provide an elementary introduction into
the main ideas underlying the physics of CME, a historical perspective, and a
guide to the rapidly growing literature on this topic.
