The term anelasticity is used to denote that property of metals in virtue of which strain is not a unique function of stress even at such low stress levels that no permanent set is observed. A review is given of the formal relations between the various anelastic effects, including those which may be measured by acoustical methods. A survey is made of the physical origin of anelasticity. One origin lies in the coupling of the elastic system with the various thermodynamic potentials of the system. A second basis lies in the presence of localized non-crystalline regions or interfaces. Emphasis is put upon the urgent need of a thorough study of the mechanical properties of these localized regions through acoustical studies.