In this paper some recent advances made in the understanding of the phenomena and computational modelling of the interaction of local and overall instabilities in stiffened cylindrical shells will be reviewed. These relate to two distinct categories of problems: (1) Axially compressed stringer-stiffened shells and (2) Ring-stiffened cylinders subjected to hydrostatic compression. The former have been analyzed with a novel methodology which employs finite elements in which the local buckling information is embedded. Comparisons of the results of the new technique with Abaqus - a well established nonlinear analysis program - reveals the validity of the underlying concepts of the new technique and efficacy of the new approach. It is shown, that provided all the key local buckling modes triggered in the interaction are considered and the modulation of local buckling amplitudes is accounted for, it is justifiable to neglect the mixed second order stresses and strains in the analysis. Imperfection-sensitivity of a stringer stiffened cylindrical shell structure is illustrated. In the case ring-stiffened cylinders subjected to hydrostatic pressure, it is shown that the amplitude modulation is the key factor in the interaction; it performs the function of capturing the contributions of several neighboring modes of the same longitudinal description as the fundamental local mode, but with differing circumferential wave numbers. An examination of the potential energy function indicates that the amplitude modulation is solely responsible for the presence of the nonvanishing cubic terms, which are dominant over the quartic terms. Once again, mixed second order fields evaluated with appropriate orthogonality conditions have little influence on the interaction and can be safely neglected. An example of an orthotropic layered shell under coincident and well separated critical stresses is presented.