Our safety, comfort and peace of mind are heavily dependent upon our capability to prevent, predict or postpone the failure of components and structures on the basis of sound physical principles. While the external loadings acting on a material or component are clearly important, There are other contributory factors including unfavourable materials microstructure, pre-existing defects and residual stresses. Residual stresses can add to, or subtract from, the applied stresses and so when unexpected failure occurs it is often because residual stresses have combined critically with the applied stresses, or because together with the presence of undetected defects they have dangerously lowered the applied stress at which failure will occur. Consequently it is important that the origins of residual stress are understood, opportunities for removing harmful or introducing beneficial residual stresses recognized, their evolution in-service predicted, their influence on failure processes understood and safe structural integrity assessments made, so as to either remove the part prior to failure, or to take corrective action to extend life. This paper reviews the progress in these aspects in the light of the basic failure mechanisms.