Large area graphene (LAG) sheets can be embedded in a polymer-based material as a mechanical reinforcement or to otherwise enhance the properties of the polymer-based material. The LAG sheets can be nanoperforated and/or functionalized to enhance interaction between the graphene and the polymer. Reactive functional groups can facilitate formation of covalent bonds between the graphene and the polymer so that the LAG sheets become an integral part of the cross-linked structure in curable polymer-based materials. Nanoperforations in the LAG sheets provide useful sites for the functional groups and can allow cross-links to form through the nanoperforations.