A comprehensive review is presented on the main analytical methods used in the specialized literature to evaluate the buckling loads of thin-walled cylindrical shells (TWCS) subjected to different mechanical loads or load combinations. The analytical formulations are first presented for unstiffened TWCS, followed by stiffened TWCS in different configurations (stiffeners in the axial direction, circumferential direction or both axial and circumferential directions, placed on the external or internal surface of the shell). This research can serve as a helpful resource for researchers investigating this field, allowing the analytical methods to be used as a reference basis for numerical and experimental results regarding the behavior of structures in the category of TWCS.