This article presents a review of the research work related to the mechanical behavior of non-circular cylindrical shells and shell segments. To this end, after a brief reference to the basic nomenclature that is mainly used, it initially provides quite a general framework for most of the relevant governing equations employed in the relevant literature. It proceeds with a review of the corresponding dynamic analyses, which are primarily grouped according to the geometrical configuration of the noncircular shell considered and secondarily according to the type of the mathematical model employed. These deal with the dynamics of closed cylindrical shells and open cylindrical panels based on classical (CST) or transverse shear deformable shell theories (SDST). The static analyses reviewed next are divided according to the nature of the physical problem considered and deal with small as well as with large deflections of statically loaded non-circular cylindrical shells. These include both linearized and geometrically nonlinear elastic stability analyses as well as the very few relevant studies that assumed an elastic-plastic response of the shell material constitution. This review article contains 196 references.