Digital twins are continuously updated virtual representations of physical objects, processes or systems that support simulation-based decision-making by establishing a two-way link between physics-driven models and real-world observational data. Although they first gained prominence in the manufacturing industry under the Industry 4.0 paradigm, digital twins have since found application in a wide range of domains among others in critical civil infrastructure such as road networks, bridges, wastewater treatment facilities, and energy grids: systems characterized by high cost, long service lives, and stringent safety requirements. Thereby, the predictive capability and operational utility of digital twins depend fundamentally on sophisticated computational mechanics, the ability to run simulations in real time, and seamless integration between data and models. Building dependable digital twins for civil infrastructure systems requires deep interdisciplinary collaboration, integrating domain-specific modeling, numerical simulation, data assimilation, and machine learning to construct, validate, and interconnect the necessary sub-models, datasets, and interfaces. In contrast to conventional simulation workflows, digital twins face the added challenges of satisfying real-time performance requirements, incorporating streaming data, and continuously updating their underlying models – tasks that become especially demanding in high-dimensional, multi-physics, or nonlinear problem settings. In safety-critical applications, achieving the levels of robustness and interpretability demanded by stakeholders places further constraints on numerical stability, uncertainty quantification methods, and the design of model hierarchies.