X-ray crystallography of 3-D bulk materials opened entire new fields of discovery in the twentieth century, from elemental crystals to DNA molecules. Similarly, the determination of atomic-scale structure of 2-D surfaces of condensed matter has achieved fundamental new understanding and generated powerful techniques that helped spawn new areas of research, from catalysis to nanotechnology, for the twenty-first century. Specific examples include, among many others: new catalysts; various new carbon structures (such as buckminsterfullerenes, nanotubes and graphene); quantum dots used in optoelectronic displays (including television displays); molecules allowing electron transport and switching; nanoparticles enabling targeted drug delivery; and nanomachines for future manufacturing and medical applications.