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In the European Union, codes and rules for guaranteeing safety and reliability of engineering structures are standardized in Eurocode EN 1990 – Basis of Structural Design. Furthermore, ASME has released the V&V 10 – 2006 Guide for Verification and Validation in Computational Solid Mechanics, treating verified and validated mathematical models as well as verified computer codes. The issues of the ASME V&V Guide are not considered in Eurocode EN 1990 yet. V&V is realized in Computational Mechanics by error-controlled model and discretization adaptivity of engineering structures, guaranteeing reliability and achieving computational efficiency. This is the main issue of this paper. In particular, expansive model adaptivity from coarse to fine mathematical models in related subdomains is reasonable and efficient, in contrast to recursive model adaptivity. Validation needs the incorporation of verified measurements from physical experiments. This paper presents a deterministic methodology for combined verification and model adaptivity by overall error control of quantities of interest. The necessary prolongation of coarse model solutions into the solution space of a fine model for defining a consistent model error is emphasized. Another noteworthy part of the paper is the structural optimization of engineering structures with elasto-plastic deformations under shakedown conditions, i.e. for load domains. This is motivated by the fact that structural optimization in the presence of elasto-plastic deformations for distinct loading paths does not make any sense. Finally, this paper also presents some design problems of a very complex structure: the German Pavilion at the World Exhibition 2000 in Hannover with principally new concave glass facades and glass-stiffened pre-stressed steel columns for supporting the huge roof. Especially the safety requirements for the various glass structures are discussed. [ABSTRACT FROM AUTHOR]