Pressure vessels comprise critical plant equipment within industrial operations. The fact that the vessel operates under pressure, and may carry toxic, dangerous or hazardous contents, necessitates that care is taken to ensure safety of humans operating it and the environment within which it operates. Residual stress developed during welding of pressure vessel structures adversely affects fatigue life of such structure by reducing fracture toughness. Formation of residual stresses during welding occurs when nonuniform heating of the metallic surfaces produces substantial temperature gradients, which in turn cause plastic straining of the different portions of the weld-piece material, thereby subjecting it to postcooling internal stresses that are likely to weaken it. A number of studies have been performed on welding parametric analysis with the help of design of experiments (DoE), mathematical programming, evolutionary algorithms and finite element methods, with the intention to quantify effects of welding factors on resultant residual stress. The objective of this review is to organize such literature according to the specific areas of analysis in order to enhance access thereto and elucidate relevance thereof for purposes of reference work and further studies. The paper specifies three categories of influential factors as prewelding conditions, in-process parameters, and postwelding conditions. It is shown that prewelding conditions, such as the choice of welding process, must be chosen in line with the nature of materials to be welded, operational application of the structure, and trade-offs between service life and production costs. Heat input (which is the function of arc voltage, welding current, and travel speed) is the most influential machine-related in-process parameter in the residual stress generation during welding. It is also observed that when applying mitigating factors, care should be taken not to exacerbate the residual stress situation through suboptimal parametric set-up.