The increasing performance requirements of modern engineering applications demand the rapid development of materials and structures with enhanced mechanical properties under strict technological and time constraints. Advances in large-scale computing and numerical modelling have enabled simulation-driven design as a flexible, cost-effective alternative to experimental testing, supporting fully automated, unsupervised workflows. High-fidelity modelling techniques, such as computational homogenisation, further enable a direct link between microscopic features and macroscopic material response, providing a rigorous multi-scale foundation for design and analysis. The effectiveness of these approaches, however, critically depends on the availability of efficient and scalable optimisation strategies. In this work, we present a composite Bayesian optimisation framework [1, 2] for the analysis and design of materials and structures. By exploiting the compositional structure of the objective function, the proposed method substantially reduces the number of required simulations or experiments, outperforming state-of-the-art optimisers. Its probabilistic formulation enables a principled treatment of uncertainty, making it well suited to stochastic objectives with noisy observations. The framework naturally supports multi-objective optimisation, allowing the systematic identification of competing trade-offs, and inverse identification campaigns using full-field reference data. We demonstrate the approach on a range of applications, including constitutive parameter identification, structural optimisation, and stochastic and multi-objective polycrystalline material design. Finally, we introduce piglot [3], an open-source Python package for derivative-free, unsupervised optimisation implementing the proposed algorithms, providing a practical pathway toward accelerating simulation-based engineering design. [1] Cardoso Coelho et al. (2024). Efficient constitutive parameter identification through optimisation-based techniques: A comparative analysis and novel composite Bayesian optimisation strategy. CMAME, 427, 117039. [2] Cardoso Coelho et al. (2025). A composite Bayesian optimisation framework for material and structural design. CMAME, 434, 117516. [3] Cardoso Coelho et al. (2024). piglot: An open-source package for derivative-free optimisation of numerical responses. JOSS, 9(99), 6652.