This review article is devoted to an analysis of the literature on the stress-strain state of shells with developable middle surfaces. Wide choices of design methods for the developable surfaces provide not only the necessary shapes and special properties; they also prove to be convenient to apply. Representative examples are given for the static analysis of thin elastic shells by both analytic and numerical methods. Generally, the curvilinear non-orthogonal conjugate coordinates of the developable middle surface are used. Lines of principal curvatures are used as coordinates only for the strength analysis of thin shells in the form of Monge’s ruled surfaces. It is shown that momentless and moment theories give similar results if certain conditions are met a priori. The parabolic (isometric) bending of thin developable shells is also analyzed. This review article contains 97 references.