It has been more than 15 years since the study outlined the main directions of development of the theory of multilayered shells. The survey analyzed investigations conducted mainly during the 1978-1981 period, but it focused principally on applied methods of design of plates and shells made of composites and questions relating to structural design. Thus, there has been a longstanding need to examine research in the theory of multilayered shells from a common viewpoint to discern the general direction of development of the theory, with most of the relevant studies having been published since 1972. The authors look at investigations in which different types of nonclassical hypotheses were used to describe the mechanical behavior of each shell layer.