The purpose of this talk is to provide an overview of the most recent theoretical studies undertaken by us in the field of hydrogen storage materials research with the focus “how high pressure” can play an important role in search and design of new hydrogen storage materials. On selected examples, the application of our computational tool of choice, density functional theory, will be illustrated to show how ab initio calculations can be of use in the effort to reach a better understanding of hydrogen storage materials and to occasionally also guide the search for new promising approaches. A deeper theoretical understanding of the catalytic mechanism involved in kinetic enhancement should be a very valuable guide in the design of new catalysts. Systems to be discussed include: Metal-organic frameworks, where we have studied hydrogen physisorption in three different types of iso-reticular MOFs, namely Zn-/Mg-/Ca-MOF16, decorated with either Li, Na, or K. Lithium ion diffusion in lithium imide (Li2NH), and lithium amide (LiNH2) studied by us using both ab initio molecular dynamics simulations and the nudged elastic band method. Finally, catalysts play an important role in many hydrogen desorption processes. We found (through a combination of experiment and theory) that carbon nanostructures, in particular nanotubes and fullerenes, can be used as catalyzing agents for hydrogen uptake and release in complex metal hydrides (such as sodium alanate, NaAlH4) and provide a model which could explain the mechanism of the catalytic effect.