Molecular-crystalline duality of graphene ensures a tight alliance of its physical and chemical natures, each of which is unique in its own way. The article examines the physical-chemical harmony and/or confrontation in terms of the molecular theory of graphene. Chemistry that is consistent with graphene physics expectations involves: small mass of carbon atoms, which provides a lightweight material; sp2 configuration of the atoms valence electrons, ensuring a flat two-dimensional structure of condensed benzenoid units; high strength of CC valence bonds responsible for exclusive mechanical strength. Chemistry that is in conflict with graphene physics expectations covers: radical character of graphene material; collective character of electronic system of graphene, preventing from localization of its response on any external impact; the molecular nature and topochemical character of graphene mechanics; the molecular nature of graphene magnetism. Each of the properties is a direct consequence of the odd electron correlation, on one hand, and ensures a high instability of graphene material, on the other. Electron correlation inhibition by deposition of graphene monolayers on substrates is seen as a promising way to solve the problem. © 2014 Wiley Periodicals, Inc.