In recent experiments we have discovered the unique ability of the two-dimensional tungsten surface carbideW(110)/C-R(15 × 3) to support self-organization of nanostructures with an extreme variety of physical and chemical properties. The goal of the current publication is to provide a comprehensive review of our recent achievements with this system. Using the technique of scanning tunneling microscopy we have observed one-dimensional self-assembly of noble and transition metals. Experiments with fullerene molecules have shown that C60 deposited on the surface carbide self-organizes into clusters with magic numbers and at higher coverage into chains. Angular-resolved photoelectron spectroscopy has provided comprehensive information about the electronic and chemical states in the self-assembled nanostructures.