A B S T R A C T In this review paper, only constraint and stress gradient approaches to transferability of fracture toughness are examined. The different constraint parameters are defined and discussed, and one example is given in each case. Factors that influence the constraint are studied. Special attention is given to the actual trends to use the plastic constraint in the material failure master curve and the material transition temperature master curve. The paper also deals on the influence of T stress on the crack path and out-of-plane constraint and on the influence of thickness on fracture toughness. The uses of plasticity with gradient and the relative stress gradient in local fracture approaches are also examined.A = constant A i = Williams' stress distribution parameterŝ A i = HRR stress distribution parameters A P = Constraint parameter A p,c = current plastic zone area A p,ssy = reference plastic zone area A εp,c = area surrounded by the equivalent plastic strain A εp,ref = reference area surrounded by the (ε p ) isolines B = thickness B 0 , B 1 , B 2 and B 3 = constants D = pipe diameter D 0 = length E = Young's modulus F = geometry correction factor G = shear modulus G c = fracture toughness I = complex function of eigenvalues I n = dimensionless integration constant J = path integral J c = fracture toughness J Ic = fracture toughness in plane strain conditions J ref = reference fracture toughness K Ic = fracture toughness for plane strain conditions K Jc = fracture toughness K Iz,c = three-dimensional fracture toughness in pure mode I K 0 = lower bound of the notch fracture toughness K ρ,c = notch fracture toughness K 0 ρ;c = fracture toughness corresponding to T ef,c = 0 L = plastic constraint factor N = strain hardening exponent