  We give an overview of the magnetic catalysis phenomenon. In the framework of
quantum field theory, magnetic catalysis is broadly defined as an enhancement
of dynamical symmetry breaking by an external magnetic field. We start from a
brief discussion of spontaneous symmetry breaking and the role of a magnetic
field in its a dynamics. This is followed by a detailed presentation of the
essential features of the phenomenon. In particular, we emphasize that the
dimensional reduction plays a profound role in the pairing dynamics in a
magnetic field. Using the general nature of underlying physics and its
robustness with respect to interaction types and model content, we argue that
magnetic catalysis is a universal and model-independent phenomenon. In support
of this claim, we show how magnetic catalysis is realized in various models
with short-range and long-range interactions. We argue that the general nature
of the phenomenon implies a wide range of potential applications: from certain
types of solid state systems to models in cosmology, particle and nuclear
physics. We finish the review with general remarks about magnetic catalysis and
an outlook for future research.
