Abstract: Hydrogen storage in lightweight hydrides continues to attract significant interest as the lack of a safe and efficient storage of hydrogen remains the major technological barrier to the widespread use of hydrogen as a fuel. The metal borohydrides Ca(BH₄)₂ and LiBH₄ form the subject of this thesis; three aspects of considerable academic interest were investigated by density functional theory (DFT) and molecular dynamics (MD) modelling. (i) High-pressure crystal structures of Ca(BH₄)₂ were predicted from a structural analogy between metal borohydrides and isoelectronic metal oxides. The structural stability of hydrogen storage materials under high pressure is an important aspect, as high-pressure polymorphs may provide structures with better hydrogen desorption properties. The isoelectronic analogue of Ca(BH₄)₂ is TiO₂, and structural equivalents of Ca(BH₄)₂ in the baddeleyite, columbite and cotunnite structures of TiO₂ were found to be stable at elevated pressure. Thermodynamic stability was evaluated by computing the Gibbs energy with respect to pressure and temperature. The pressure-dependence of the Helmholtz energy was determined to described a third-order Birch-Murnaghan equation of state, and the harmonic approximation was used to compute the vibrational energy levels and the Helmholtz energy as a function of temperature. The proposed structures are consistent with reports of two hitherto unidentified high-pressure phases observed experimentally. (ii) The disordered structure of the high-temperature phase of LiBH4 was studied by ab initio molecular dynamics (MD) at temperatures ranging from 200-535 K. It was found that the model emerging from analysis of the MD simulations properly accounts for dynamical disorder and fundamentally differs from the published experimental and theoretical structures. The validity of the MD model was corroborated by comparison of calculated pair distribution functions, vibrational spectra and a crystallographic model with neutron diffraction data; good agreement was found. A reassignment of the space group from P63mc to P63/mmc is proposed based on evidence for additional symmetry from MD simulations. (iii) Finally, a new MD-based method was developed to simulate fast ionic diffusion in LiBH₄. The colour diffusion algorithm - a nonequilibrium molecular dynamics method originally developed for the study of model fluids - was adapted and applied to self-diffusion of atoms in a solid for the first time. Calculated diffusion coefficients agreed very well with published measurements, and diffusion pathways that include collective particle effects were determined directly from the simulation results, thereby opening up a promising and efficient new method for the study of phenomena such as superionic conduction.