The chapter is devoted to the chemical uniqueness of graphene. In view of molecular theory, the uniqueness is a consequence of benzenoid packing of carbon atoms, based on three neighbors to each carbon atom leaving the atom fourth valence electron (the odd one) on its own. Due to rather large C-C distances, the odd electrons of graphene molecules are correlated whereupon the molecules are radicalized, and molecular chemistry of graphene is the chemistry of "dangling bonds." The chapter presents the description of the molecular-theorydangling- bond view on graphene molecule hydrogenation and oxidation. Specific peculiarities of the graphene molecular chemistry related to size-dependent topochemical features are discussed, as well. © 2016 by Taylor & Francis Group, LLC.