A discussion is given of the three general approaches to the theory of the acoustoelectric effect-the equilibrium, the transport, and the phenomenological approaches. The fact that these three approaches have led to mutually conflicting conclusions is due to three causes. (1) The last approach is applicable only when the mean free path of the charge carriers is much smaller than the acoustic wavelength; the first two approaches, only when the mean free path is much greater than the wavelength. (2) The transport approach of necessity ignores the contribution of charge carriers "trapped" by the acoustic wave. (3) The phenomenological approach, as developed in the previous literature, ignores the contribution to the space-charge density coming from the ion-cores of a metal or the ionized impurity atoms of a semiconductor. In this paper a development of the phenomenological approach is given in detail for metals and for semiconductors. This is the approach appropriate under most experimental conditions, but at sufficiently low temperatures and high acoustic frequencies the equilibrium approach is appropriate in metals and semimetals. It is pointed out that the acoustoelectric effect may be considerably enhanced by the application of a magnetic field.