Two fundamental properties, strength and wettability, of graphene will be reviewed and discussed from theoretical perspectives. While the ideal intrinsic strength of single crystal graphene is theoretically predicted and mechanically measured by nanoindentation to be 120 GPa, there are still debates on whether the polycrystalline graphene is as strong as its single crystalline counterpart or not. Another property on the debate was the wetting transparency of graphene, the transmission of the substrate wetting property over graphene coating. In the present work, based on the combined theoretical and atomistic modeling approaches, we will resolve the controversy over the two fundamental properties of graphene.