Hydrogen is ubiquitous in catalysis. It is involved in many important reactions such as water splitting, N2 reduction, CO2 reduction, and alkane activation. In this Perspective, we focus on the hydrogen atom and follow its electron as it interacts with a catalyst or behaves as part of a catalyst from a computational point of view. We present recent examples in both nanocluster and solid catalysts to elucidate the parameters governing the strength of the hydrogen-surface interactions based on site geometry and electronic structure. We further show the interesting behavior of hydride in nanometal and oxides for catalysis. The key take-home messages are: (1) the in-the-middle electronegativity and small size of hydrogen give it great versatility in interacting with active sites on nanoparticles and solid surfaces; (2) the strength of hydrogen binding to an active site on a surface is an important descriptor of the chemical and catalytic properties of the surface; (3) the energetics of the hydrogen binding is closely related to the electronic structure of the catalyst; (4) hydrides in nanoclusters and oxides and on surfaces offer unique reactivity for reduction reactions.