The work deals with a systematic theoretical and problem-oriented treatment of fundamental topics in the wide area of error-controlled adaptive finite element methods for analyzing engineering structures with elastic and inelastic material behavior applied to engineering structures. Different types of error estimators are presented from both mathematical and engineering points of views: global estimators and goal-oriented estimators based on duality techniques, controlling h-, p-, and hp-adaptivity. Special features are: combined model and discretization adaptivity for thin-walled structures, hierarchic modeling in elasticity and related hp-adaptivity, error estimators of constitutive equations, adequate mesh refinement techniques and error-controlled adaptive elastic-plastic analysis of contact problems. The benefits are seen in new methods and results of leading researches in the field which provide deeper insight into recent developments of a posteriori error analysis and adaptivity.