Functional surfaces and nanostructures play an increasingly important role in nanoscience and nanotechnology.Here we report on the rational design of these structures via supramolecular self-assembly employing non-covalent interactions,e.g.,hydrogen bonding,ionic bonding and metal-ligand coordination bonding.0-,1-and 2-dimensional systems with specific topologies and physical/chemical characteristics have been prepared under ultra-high vacuum conditions by organic molecular beam epitaxy.Scanning tunneling microscopy has been used to study these unique systems in-situ.First the assembly principles involving of different types of interactions have been studied.Then we apply these principles to fabricate nanostructures providing pre-designed structures and properties.We also explore the potential functionalities of the low-dimensional supramolecular systems.For instance,network structures comprising of 2-D nanoscale cavities may selectively host specific guest molecules.The relevant recognition principles of the host-guest interactions can be studied by STM on the atomic scale.Further examples include novel magnetic and catalytic properties of the periodically organized iron atoms or atom-pairs embedded in the metal-organic architectures.