Computational models play a central role in the simulation, design, and control of complex engineering systems. As these systems grow in complexity, there is a growing demand for efficient and accurate numerical methods; furthermore, real-time prediction, multi-query scenarios, and large-scale optimization and control remain challenging for conventional high-fidelity solvers due to their prohibitive computational cost. Reduced-order models (ROMs) offer a promising path forward by providing significant computational savings while preserving essential features of the underlying high-dimensional systems. This minisymposium aims to explore recent advances in high-order discretization techniques and reduced-order modelling approaches, with a focus on challenging applications in computational fluid dynamics, structural mechanics, and multiphysics problems. Of particular interest are high-order methods that offer superior accuracy per degree of freedom, and model order reduction strategies that remain robust over wide parameter ranges or preserve critical structures such as conservation laws, symmetries, positivity or entropy. Topics of interest include, but are not limited to: projection- and collocation-based model reduction techniques for parametric systems; hyper-reduction strategies; structure-preserving high-fidelity numerical schemes and ROMs for nonlinear PDEs; high-fidelity discretization tailored for reduced-order modelling; data-driven and hybrid machine learning-ROM and deep-learning approaches; adaptive and error-controlled model reduction; applications to control, uncertainty quantification, inverse problems, and digital twins. Bringing together researchers working at the interface of numerical analysis, scientific computing, and engineering applications, this minisymposium will provide a forum for the presentation and discussion of recent methodological developments, benchmarking efforts, and cross-disciplinary applications. A key objective is to foster a shared understanding of the respective roles and limitations of high-fidelity and reduced-order models, promoting their synergistic integration in simulation pipelines. This perspective is essential to enable the next generation of predictive, efficient, and adaptive computational methods.