An introductory review of the central ideas in the modern theory of dynamic critical phenomena is
followed by a more detailed account of recent developments in the field. The concepts of the conventional
theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are
illustrated in the context of a simple example—the phase separation of a symmetric binary fluid. The
renormalization group is then developed in some detail, and applied to a variety of systems. The main
dynamic universality classes are identified and characterized. It is found that the mode-coupling and
renormalization group theories successfully explain available experimental data at the critical point of pure
fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies
exist with data at the superfluid transition of 4He.