2D supramolecular self-assembly has emerged as a powerful tool in nanoscience for bottom-up fabrication of well-defined and long range ordered two-dimensional (2D) molecular nanostructures at surfaces. Following an overview of the principles of this distinctive self-assembly process, this review focusses on recent stategies developed to go beyond the surface nanopatterning and to provide functional surfaces. With an emphasis on the chemical engineering of the molecular building-blocks constituting the adlayer, we show that besides supported nanoporous networks the more promising approach lies on up-standing 3D functional build-blocks mounted on the substrate. We highlight the opportunities offered by graphene, a substrate for which the non-covalent functionalization by supramolecular self-assembly represents a way to either control its electronic properties or provide it a new functionality. Finally, future perspectives are addressed.