This article contains a survey of some of the recent literature on the structural integrity of metallic and composite domed closures subjected to external or internal pressure. The article refers to other recent reviews and gives a general overview of recent and current research with which the author has been directly or indirectly concerned. For externally pressurized heads this includes correlation between experimental and numerical results, imperfection sensitivity, low buckling resistance of shallow torispheres, and modelling of wound and handdraped multi-ply composite domes. For internally pressurized heads, the topics include the plastic buckling paradox, plastic loads and first cycle shakedown pressures. Structural optimization of vessel closures is also mentioned in the article. Progress in Structural Engineering and Materials I998 Vol I(4): 4 I 5-42 I