We review the physical mechanisms that lead toward the conversion of graphene into its fully hydrogenated counterpart, which is a material that possesses properties closer to those of diamond than graphene. These are discussed from a theoretical perspective, i.e., from calculations based on density functional theory. We first discuss stability trends in small clusters of adsorbed hydrogen, as well as surface structure and concurrent reactivity changes for graphene one-face and two-face hydrogenation. Effects of adsorbed hydrogen on graphene electronic states, which are essential to adsorbed hydrogen structure discrimination, are also discussed.