Hydrogen combustion offers a promising route to the decarbonisation of future aeronautical propulsion systems, yet its application in practical aeronautical injectors remains challenged by strong thermo-diffusive effects, enhanced flame instabilities, and complex turbulence–chemistry interactions. Advanced simulation technologies are therefore required to achieve predictive capability under realistic operating conditions. High-fidelity modelling strategies are employed to capture the unsteady flow–flame dynamics governing flame stabilisation, mixing, and heat release, as well as their sensitivity to injector design and operating conditions. Particular attention is devoted to the modelling of differential and preferential diffusion effects, which play a central role in lean hydrogen flames and strongly influence flame topology, burning velocity, and local extinction–reignition processes. The LES framework combines detailed or tabulated chemistry with advanced subgrid-scale closures suitable for low-Lewis-number fuels, enabling an accurate representation of turbulence–chemistry interaction in aeronautical injectors. Owing to the high computational cost associated with resolving these coupled multi-scale processes, the simulations are conducted in high-performance computing (HPC) environments, with increasing emphasis on GPU-accelerated architectures to enable large-scale, time-resolved LES at realistic Reynolds numbers and geometric complexity. Overall, the results demonstrate the capability of state-of-the-art LES, supported by modern HPC and GPU technologies, to provide both physical insight and quantitative predictions for hydrogen combustion in aeronautical injectors, supporting the development of robust, low-emission combustion concepts for next-generation aircraft engines.