Gas hydrates consist of hydrogen-bonded water frameworks enclosing guest gas molecules and have been the focus of intense research for almost 40 years, both for their fundamental role in the understanding of hydrophobic interactions and for gas storage and energy-related applications. This research project is focused on the water-hydrogen compound (hydrogen hydrate). Hydrogen hydrates can trap hydrogen at mass fractions competing with those of the best materials presently used for hydrogen storage, having the advantage of being environmentally friendly. Pressure is a key parameter in the study of hydrogen hydrates as it remarkably increases their temperature range stability and their storage capability, and it induces substantial variations in the water-hydrogen distances as well as structural transitions. The aim of our project is to apply a combination of experimental techniques, including X-ray and neutron diffraction, quasi-elastic neutron scattering, Infrared and Raman spectroscopy, to characterise the structural stability of H2 hydrate structures, their H2 up-taking, and the new H2-rich structures it forms under HP. The outcomes of this project will be also applicable to a more profound understanding of planetary interiors where H2-H2O hydrates under HP are largely present at depths.