In the context of computational engineering, physical systems are classically represented by a mathematical model which can be picked in a hierarchical list of possible models, with increasing complexity, and which is then numerically processed to obtain a virtual twin. In such a framework, a critical error source comes from imperfect modeling. Therefore, for safe decision-making, there is a need for certification of the predicted outputs, with consistency between physical reality and numerical models; this is the matter of model parameter updating, but also model enrichment in order to correct model bias from data-based information (hybrid approach). On the other hand, there is a need for effectivity, in order to perform fast data assimilation and control as required in Dynamic Data Driven Application Systems (DDDAS) in which a continuous exchange between simulations and experimental measurements is implemented. The goal is thus to compute right at the right cost, with smart management of computing resources depending on the objective and complexity of the observed physical phenomena. This resorts to model adaptivity and suitable selection of a reference mathematical model in view of experimental data. The talk addresses these various topics by using the Constitutive Relation Error concept. In its modified version [Ladeveze99,Marchand19], it is a powerful, relevant, and robust tool to perform suitable modeling and simulation with respect to experimental information. During the presentation, the philosophy and performance of this tool will be shown on several recent mechanical engineering applications related to (sequential) model parameter updating with noisy data (e.g. [Diaz21]), but also data-based model selection and correction with regards to rich data coming from full-field measurements or distributed optic fiber sensing. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 101002857) [Ladeveze99] Ladevèze, P., Chouaki, A. Application of a posteriori error estimation for structural model updating. Inverse Problems (1999) 15(1): 49-58. [Marchand19] Marchand, B., Chamoin, L., Rey, C. Parameter identification and model updating in the context of nonlinear mechanical behaviors using a unified formulation of the modified Constitutive Relation Error concept. Comput. Methods Appl. Mech. Eng. (2019) 345: 1094-1113. [Diaz21] Diaz, M., Charbonnel, P-E., Chamoin, L. Robust energy-based model updating for random processes in dynamics: application to shaking-table experiments. Comput. \& Structures (accepted).