This paper describes the methods of analysis of bolted flanged connections of pressure vessels and piping, as they are used in various industrialized countries. Discussed are early methods (Bach, Timoshenko, Waters-Taylor, etc.), methods using an elastic analysis (ASME Code), elasto-plastic methods (Lake and Boyd, Schwaigerer) and some simplified methods.Flat face flanges with metal-to-metal contact outside the bolt circle, in matched and dissimilar pairs (ASME Code Case No. 1828), as well as gasketed joints, with gaskets extending outside the bolt-circle (so-called full face gasketed joints) are included. Information on gasket and bolting literature and computer methods is given.