Abstract: Thin cylindrical shells under axial compression are commonly found in a wide range of civil engineering steel shell structures, including silos, towers, chimneys and tanks. Buckling of axially compressed cylindrical shells has been one of the most active areas of shell buckling research. This paper provides a review of advances in stability research on axially compressed cylinders and in the development of design rules. Classical studies on the buckling of axially compressed cylindrical shells and the imperfection sensitivity of these shells are first introduced, followed by a summary of existing work on the relationship between the manufacturing process and the induced imperfection in a real shell, as well as the effect of residual stresses. The main focus of the paper is however to introduce the design rules for axially compressed cylinders in the new European code for steel shell structures, and to present the background information on which these rules were based.