Theoretical studies have been carried out to examine hydrogen storage in some binary transition metal alloys which include titanium as one of the alloying elements. Quantum mechanical calculations at the Extended Huckel level of approximation have been performed on numerous clusters of compositions Ti18Ni18, Ti18Ni18H, Ti18Ni18H12, Ti24Ni12, Ti24Ni12H, Ti24Ni12Hi12, Ti16Cu16, Ti16Cu16H, Ti24Cu2, Ti16Fe16, Ti16Fe16H9, and Ti16Fe16H32, to yield information on energetics, densities of states, charge distributions, and the effects of hydrogenation on these properties. In addition, ab initio calculations at the split valence level of approximation have been performed on several smaller clusters. The hydrogens have been shown to acquire a partially anionic character in all cases. Another conclusion is that the preference of H for certain types of sites (for example the tetrahedral Ti4 sites in crystalline TiCu) is more likely to be related not to the intrinsically greater stability of a hydrogen atom located in such a site, but to more general topological and electronic considerations. Qualitative concepts related to the classification, spatial distribution, and sizes and shapes of “hole” sites which could become occupied by hydrogen atoms, have been shown to correlate with hydrogen storage capacity for crystalline materials. These qualitative concepts have been extended to amorphous materials and corroborate the observations that under optimized conditions amorphous alloys can be found with better reversible hydrogen storage properties than the crystalline or microcrystalline systems. Distorted tetrahedral and octahedral holes have been examined in detail, and parameters (volume, area, “tetrahedrality”, and “octahedrality”) have been introduced to describe their sizes and shapes. An algorithmic surveying technique has been introduced, and shown to provide useful information about the limiting amounts of hydrogen uptake.