A systematic theoretical study on the molecular electronic structure of graphene and its oxides, including their interactions with molecular species of different polarity, was carried out. The influence of the O/C atomic ratio in the graphene oxides was also evaluated. Quantum chemical and COSMO-based statistical-thermodynamic calculations were performed. Geometry optimizations demonstrated that graphene sheets are structurally distorted by oxygen substitution, although they show high resistance to deformation. Furthermore, under axial O-C bonding, proton-donor and proton-acceptor centers are created on the graphene oxide surface, which could acquire an amphoteric character. In low-oxidized graphene oxides, H-bonding centers coexist with neutral highly polarizable π electron clouds. Deep graphene oxidation is also related to the formation of a -two-dimensional H-bond network. These two phenomena are responsible for the exceptional adsorption and catalytic properties and the potential proton conductivity of graphene oxides. The current calculations demonstrated that the interactions of polar molecular species with deep-oxidized graphene derivatives are thermodynamically favorable, but not with low-oxidized ones. The capacity of the quantum chemical and COSMO-RS calculations to model all these issues opens the possibility of selecting or designing graphene-based materials with optimized properties for specific applications. Also, they are valuable in selecting/designing solvents with good exfoliant properties with respect to certain graphene derivatives.