The rapid advancement of innovative numerical methods and cutting-edge technologies has revolutionised the development of advanced materials and structures, enabling them to be precisely tailored for specific applications. In material design, the core objective is to meticulously select the chemical structure, composition, and processing conditions to achieve challenging design criteria. These criteria often focus on optimising key properties such as toughness, strength, and durability while simultaneously minimising cost, weight, and environmental impact. In structural design, similar principles are applied to ensure that the architecture of materials and components not only meets functional requirements but also enhances performance, safety, and efficiency across a wide range of applications, from aerospace to civil engineering and beyond. This mini-symposium aims to bring together researchers working on state-of-the-art topology, shape optimisation techniques and material design. Participants will have the opportunity to exchange ideas, present novel developments, and discuss recent advances in the field. Topics of interest include but are not limited to: • Manufacturing constraint modelling, • Multi-scale and multi-physics optimisation for metamaterials, • Optimisation of functional properties (thermal, acoustic, fluid, etc.), • Incorporating material microstructures into topology optimisation, • Structural and multidisciplinary applications, • Multi-material topology optimisation, • Modelling of manufacturing defects, • Machine learning-assisted, data-driven, and surrogate-based topology and shape optimisation • The integration of computational methods with experimental data to enhance material performance and structural efficiency. • Simultaneous material and structure optimisation • Design of nonlinear materials • Smart material design