The Digital Twin is a cornerstone technology concept within the ongoing 4th industrial revolution. By connecting physical assets to their digital replicas, Digital Twins offer unprecedented opportunities for innovation in industrial design and operation, for example, with respect to design optimization, decision support, and online (real-time) monitoring, to name but a few relevant applications. To enable disruptive Digital Twin innovations, methods stemming from the fields of scientific computing and computational science and engineering are continuously developed and optimized to address the corresponding challenges. This minisymposium aims to address novel developments with respect to computational methods that are crucial for the realization of Digital Twins and their application for challenging industrial problems. Exemplary topics of interest include: (a) Executable Digital Twins by means of model order reduction, reduced order modelling, or surrogate modelling, such that fast albeit accurate model evaluations during system operation are possible. (b) Uncertainty-aware Digital Twins by means of probabilistic simulation, uncertainty propagation, and (Bayesian) model calibration. (c) Hybrid Digital Twins that fuse physic-based and data-driven modelling, simulation, and optimization methods, thus combining “the best of two worlds”. This list is by no means exhaustive, and several other topics of interest can also be considered, provided that they feature a connection to Digital Twin technologies and applications.