Recent research effort into some aspects of strength, static stability, and structural optimization of horizontal pressure vessels is reviewed in this paper. Stress concentrations at the junction of cylinder-ellipsoidal end closures are covered in detail. This in turn establishes efficient choices for wall thicknesses in the vessel. Detailed account of stresses for flexible supports of a horizontal cylindrical shell is provided. Dimensions of support components, which assure the minimum stress concentrations between a horizontal shell and its support, are calculated. In particular, the wall thickness is found for vessels being loaded by the weight of its content and placed on two supports. Stability issues are also reviewed in this paper. In particular, attention is paid to the stability of cylinder under external pressure and to the stability of end closures. The latter are loaded by internal or external pressure. Apart from buckling and plastic loads, the ultimate load carrying capacity, i.e., burst pressure, for internally pressurized heads is also examined. On a practical side, aboveground and underground cases are discussed. In the latter case of underground vessels the reinforcement by internal rings is assessed. The optimization part of this paper deals with the effective choice of the end closure depth and the shape of its meridian. The overriding aim here is to examine the stress concentrations and the ways in which they can be mitigated. The optimal shape of closures is also searched for, with respect to the maximum buckling pressure for a given mass of the head. In the case of internal pressure the maximum of plastic load is sought within a specified class of meridional profiles. Finally, optimal sizing of whole vessels is discussed for slender and compact geometries. Extensive references are made to relatively recent and ongoing work related to the above topics. This paper has 287 references and 50 figures.