Use of the first operating linear induction accelerators (LIA) in the USA and the USSR has shown that the principle on which the operation of these accelerators is based'permits relativistic electron beams of hundreds or thousands of amperes to be obtained with efficiencies of tens of percent with high reliability and reproducibility of the results. A number of laboratories are carrying on intensive development of accelerators of this type and developing their theory, methods of calculation, and refinement of the designs. The present review systematizes and generalizes the results of published articles in this field. The article discusses the theory of LIA, the shape of the accelerating field, and the containment of the transverse dimensions of a high-current beam. The parameters are given for accelerators in operation and under construction and the design of the basic elements is described.