This EUROMECH Colloquium aims at overviewing methods and techniques dealing with different aspects of quantifying uncertainty in computational mechanics simulations. Topics relevant to the scope of this colloquium include, but are not limited to, statistical methods for uncertainty quantification, propagation and multiscale inverse problems, Bayesian inference and regularization, regression, projection and extrapolation, real-time data fusion, acceleration methods for large-scale (industrial) applications (model order reduction), model updating and model selection, virtualization of physical systems, and more.