  In this review we study quantum field theories and conformal field theories
with global symmetries in the limit of large charge for some of the generators
of the symmetry group. At low energy the sectors of the theory with large
charge are described by a hybrid form of Goldstone's theorem, involving its
relativistic and non-relativistic forms. The associated effective field theory
in the infrared allows the computation of anomalous dimensions, and operator
product expansion coefficients in a well defined expansion in inverse powers of
the global charge. This applies even when the initial theory does not have a
reliable semiclassical approximation. The large quantum number expansion
complements, and may provide an alternative approach to the bootstrap and
numerical treatments. We will present some general features of the symmetry
breaking patterns and the low-energy effective actions, and a fairly large
number of examples exhibiting the salient features of this method.
