J-R curves are used to assess the stability of growing cracks in ductile materials. Since initiation and crack-extension resistance are geometry dependent any transfer of the measured data to a structural component is subject to the individual responsibility of the engineer. The introduction of a second parameter for failure assessments beyond J-control has, therefore, been widely discussed, recently, and different approaches have been used to quantify the local stress triaxiality and crack tip constraint. Three basic ideas underline these various approaches, -including higher order terms in the analysis of asymptomatic fields at the crack tip, - utilizing the J-CTOD relationship as a measure of crack tip constraint, - considering micro-mechanisms of ductile failure. Before adding new results of tests or calculations to the existing ones it seems worthwhile to discuss the different concepts with respect to their advantages and drawbacks, limitations and generality of application, physical evidence, etc. It seems that constitutive models of damage have the highest degree of physical evidence and the generality of applications. Constraint effects do not even arise as separate problems since triaxiality of stresses enters the model directly. The investigation of micro-mechanical mechanisms helps to identify significant parameters.