The relentless demand for next-generation materials has sparked the quest for innovative and rapid design strategies. Recent breakthroughs in high-performance computing, machine learning, and simulation accuracy have shaped materials and structural design into a fundamentally computational endeavour. In this evolving landscape, high-fidelity multiscale models have become indispensable, seamlessly bridging complex microstructural features with macroscopic responses and enabling the solution of inverse problems that tailor microstructures to achieve performance targets. This thesis introduces a novel data-driven framework for the analysis and design of materials, with a particular emphasis on polycrystalline microstructures. Central to this thesis is the development of an open-source Python package, piglot, which seamlessly combines unsupervised numerical simulations with a novel composite Bayesian optimisation algorithm. Extensive numerical experiments demonstrate that our methodology not only outperforms classical optimisation methods but also significantly enhances computational efficiency and design accuracy in complex material systems. The research also addresses the complex challenge of constitutive modelling for the austenite-to-martensite transformation coupled with slip plasticity. Traditional models often simplify martensite as a brittle, purely elastic phase, leading to local stress overestimations in fully transformed regions. To overcome this shortfall, the model in [1] is extended to incorporate slip plasticity within the martensitic phase, resulting in a more robust and accurate representation of the material behaviour. A series of compelling examples demonstrates the utility of the developed framework in solving inverse problems related to constitutive parameter identification and the design of polycrystalline microstructures. Validation against experimental data confirms the model's strong predictive capabilities for stress responses, while also revealing areas for improvement in capturing the martensite volume fraction. Additionally, the framework is applied to optimise a dual-phase ferrite-martensite steel, successfully identifying the optimal phase mixture for maximum energy absorption. Overall, this thesis represents a significant step forward in computational materials design, offering robust tools and methodologies that pave the way for the rapid development of advanced materials tailored to meet emerging engineering challenges.