The sustainable transformation of multiple technological domains is one of the key challenges of this century. Achieving this goal requires an enhancement of the structural performance with respect to predefined criteria. The growing emphasis on sustainability in engineering design, combined with the rapid development of computational methods in engineering mechanics, has fueled the adoption of numerical structural optimization approaches. These methods provide a powerful and versatile tool kit for meeting the demands of present-day engineering. This minisymposium focuses on current methodological advances in numerical structural optimization. Shape and topology optimization stand as prominent examples, accessible through a multitude of different approaches and enabling the creation of highly efficient, material-saving designs across diverse application domains. Current research expands upon classical formulations by incorporating innovative materials, multi-material concepts, optimization across multiple length scales, manufacturing requirements, and multi-physics coupling to address complex, real-world scenarios. These developments are essential for unlocking the full potential of contemporary technological capabilities. The contribution of computational innovation to the accomplishment of sustainability goals defines the focal point of the session. In doing so, it will not only showcase the state of the art in numerical structural optimization but also highlight its vital role in shaping the next generation of engineering solutions for a sustainable future. The scope of the session includes, but is not limited to, theoretical developments, innovative optimization algorithms, unusual application contexts or problem formulations, and novel parametrizations. Researchers active in this forward-looking field are cordially invited to present their latest findings and engage in fruitful discussions aimed at shaping the future of sustainable engineering solutions.