High-fidelity modelling and simulation have profoundly transformed the area of material and structural design. Through advances in computer hardware and software, material failure can be reliably predicted using multiscale high-fidelity models coupled with appropriately designed discretisation strategies. Yet, such heavy numerical tasks are restricted to “one-shot” virtual experiments. Emerging applications such as real-time control or interactive design require performing thousands of repeated analyses, with potentially limited computational facilities. Models used for such applications require extreme robustness and swiftness of execution. To unleash the full potential of high-fidelity computational mechanics, we need to develop a new generation of numerical tools that will bridge the gap between, on the one hand, heavy numerical solvers and, on the other hand, computationally demanding “online” engineering tasks. This thesis introduces and summarises research contributions that aim to help bridge this gap, through the development of robust model reduction approaches to control the cost associated with multiscale and physically detailed numerical simulations, with a particular emphasis on reliability assessment for composite materials and fracture.