A survey of the approaches which have been developed for mitigating transport in stellarators is presented. A primary deficiency of stellarators has been elevated transport levels due to their nonaxisymmetry. Since the early 1980s, stellarator research has addressed this difficulty, developing a range of techniques for reducing transport, both neoclassical and, more recently, also anomalous. Several of these approaches are now being implemented in a new generation of experiments in the United States and abroad. This paper describes the fundamental physics of these methods for transport reduction.