The strength and deformation behavior of specimens and components is, on the one hand, influenced by the local state of stress and strain, and on the other hand, by the chemical composition and the microstructure of the material used. Using two different steels, it was investigated how far it is possible to predict the failure behavior of specimens and components qualitatively and quantitatively by means of local approaches. For this purpose, two methods differing considerably from the basic idea were chosen. For the description of the failure behavior, so-called damage models were used. These damage models try to describe numerically the process developing microscopically and finally leading to fracture by means of continuum mechanical approaches in order to calculate the macroscopical failure behavior. The results show that for ductile materials, the damage models allow a very accurate calculation of smooth and notched specimens and components. The efforts presently required for the calculation are, however, still very high. Analyses using fracure mechanics approaches (J-integral) in combination with the local stress states (multiaxiality) were performed to describe the failure behavior. With this approach, it was attempted to calculate crack initiation and maximum load of pre-cracked specimens and components. The fracture mechanics methods are preferred for cracked components if an engineering estimation of crack initiation and maximum load only is required since the calculation efforts of the fracture mechanics methods are much lower than those of the damage models.