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In a sustainable economy built on renewable energy, hydrogen plays a key role for storing energy and replacing fossil fuels. An efficient way to store hydrogen is to keep it in the solid state by binding it chemically in a metal hydride, which is particularly useful for seasonal energy storage or for applications where safety is a concern. Since experimental studies with hydrogen can be challenging and time-consuming, computational tools are extremely valuable for gaining a deeper understanding of the processes underlying the (de-)hydrogenation reaction. In this seminar, I will highlight our recent work on predicting the thermodynamics, interface energies, and volume expansion of metal-hydrogen systems using different computational methods. We leverage available experimental and computational data to build machine learning models as well as more sophisticated thermodynamic models for the calculation of phase diagrams (CALPHAD) to find novel metal hydride compositions and fine-tune existing alloys. Additionally, atomic-scale calculations based on density functional theory (DFT) are employed to model interfaces between the metal and hydride phases to inform meso-scale models and gain insights into nucleation barriers. As hydrogen is the lightest element of the periodic table, we also perform simulations that go beyond the classical approximation and test what happens if we treat the whole hydrogen atom as a quantum object instead.