As fatigue damage is a local phenomenon, the design of components must put emphasis on local supportable stress/strain values. In critical areas of components, because of local stress/strain concentrations and appertaining stress/strain gradients, much higher local values can be allowed than the usual design data obtained with unnotched specimens. Only the knowledge of these local values can realize light-weight design exploiting the material limits.Using component examples like pressure vessels, gears and wheel-hub assemblies, different variants of local concepts, i.e. strain and stress based methods, are presented for assessing their structural durability. For this, an interaction of numerical and experimental procedures, supported by experience, is necessary.Key words: Low-cycle fatigue, high-cycle constant amplitude loading, variable amplitude loading, contact rolling fatigue, fretting, stress and strain based local concepts, pressure vessels, gears, wheel-hub assemblies, structural durability.