Digital Twins (DTs) are sophisticated virtual representations of physical systems that dynamically integrate real-time data, computational models, and predictive analytics to enhance decision-making, optimize performance, and improve reliability. The development of DTs necessitates a seamless fusion of mathematical modeling, numerical simulation, and data-driven methodologies to ensure high fidelity, adaptability, and computational efficiency. This minisymposium aims to explore recent advancements in the mathematical and computational foundations of Digital Twins, addressing critical challenges such as model accuracy, real-time data assimilation, and computational scalability. Central topics include the mathematical modeling and numerical methods essential for accurately capturing the complexities of physical systems, with an emphasis on multi-scale and multi-physics formulations. High-performance computing (HPC) strategies and Reduced Order Models (ROMs) are crucial for enabling real-time simulation, thereby making Digital Twins practical for time-sensitive applications. Furthermore, data assimilation techniques play a pivotal role in integrating experimental and operational data into digital twin frameworks, enhancing their predictive capabilities. Uncertainty Quantification (UQ) methods provide a rigorous framework to assess, manage, and reduce uncertainties inherent in DT predictions, ensuring their robustness and reliability. The impact of Digital Twins spans a wide array of domains, revolutionizing industries, environmental sciences, and medicine. In industrial applications, DTs enable predictive maintenance, process optimization, and efficiency improvements in fields such as aerospace, energy, naval engineering, and advanced manufacturing. In environmental science, DTs facilitate real-time monitoring and forecasting of climate dynamics, disaster management, and the sustainability assessment of critical infrastructures. In medicine, patient-specific Digital Twins are transforming healthcare by enabling personalized diagnostics, treatment planning, and surgical simulations, thus enhancing precision medicine and patient outcomes. By bridging applied mathematics, computational science, and practical applications, this minisymposium seeks to foster interdisciplinary discussions on state-of-the-art methodologies and their real-world implementations.