This paper presents a brief review of recent developments in the studies of fully hydrogenated graphene sheets, also known as “graphane,” and related initial results on partially hydrogenated structures. For the fully hydrogenated case, some important discrepancies exist between published first-principles calculations, and between calculations and experiment, with qualitative differences on whether or not the graphene sheet expands or contracts upon hydrogenation. The lattice change has important effects on partially hydrogenated structures. First-principles calculations of ribbon structures, with interfaces between graphane and graphene regions, show that the interfaces have substantial misfit strains. Calculating the interfacial energy must carefully account for the strain energy in the neighboring regions, and for sufficiently large regions between interfaces, defects at the interface that relieve the strain may be energetically preferable. Tight-binding simulations show that at ambient temperatures, segments of graphene sheets may spontaneously combine with atomic hydrogen to form regions of graphane. Small amounts of chemisorbed hydrogen distort the graphene layer, due to the lattice misfit.