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Undercuts are geometrical discontinuities or grooves along the toe of a weld caused by loss of the parent material that remain unfilled by weld metal. Regardless of their causes, undercuts can be found in structures and components, in the majority of joints and most of the welding processes. Due to their frequency of appearance in welded structures and their detrimental effects on component life, undercut acceptance criteria had to be regulated by construction codes and standards. Depending on the area where the component is in service, specific tolerances must be satisfied in order to accept or reject the part. In general, undercut depth is considered to be the limiting parameter for this kind of imperfection. However, there is currently in industry no agreement about which value of depth is tolerable for a desired fatigue strength. The purposes of the present paper are twofold. First, to summarise the state of art associated to undercut tolerances in different codes, standards and recommendation documents, for different industries and applications. Secondly, to employ a fracture mechanics based methodology to predict safe undercut dimensions for butt welds subjected to fatigue. Predictions are in good agreement with experimental results from literature, and proposed method proved to be helpful for assessing weld discontinuities.