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A safe and robust performance is a key criterion when building and maintaining structures and components. Ensuring this criterion at different stages of the lifetime can be supported by applying continuous monitoring concepts. The latter usually can serve multiple purposes, including the determination of material parameters for the design phase, the evaluation of the actual loading/environmental conditions (instead of using conservative estimates that are usually larger) and evaluating or predicting the true performance of the structure (thus decreasing the model bias). In this context, a digital twin of the structure has many benefits. In addition, it allows to introduce virtual sensors to “measure” sensor information that is e.g. inaccessible or unmeasureable. In the limit, the remaining useful life of a structure can be interpreted as a property that can be “measured” indirectly via the numerical model in combination with real sensor data. In order to efficiently use monitoring techniques in the context of a digital twin, it is important to consider the complete chain of information including the choice of sensors, the data processing and structuring, the modelling assumptions, the numerical simulation and finally the stochastic nature of the model prediction. In this presentation, challenges in this context are discussed with a specific focus on Bayesian model updating of the digital twin, accounting for both parameter updates as well as model bias that results from the limitations of modelling assumption. A bottleneck in this approach is the computational effort related to sampling methods such as Markov chain Monte Carlo methods that require many evaluations of the forward model. An alternative to the expensive computation of the forward model for updating the digital twin is the combination with model reduction techniques such as the Proper General Decomposition. The results are illustrated for several examples and scales, ranging from digitals twin for material tests in the lab over lab scale structural digital twins up to damage identification in field experiments.