Recent advances in low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) have provided new opportunities for the investigation of the local geometric, electronic, magnetic, and optical properties of nanostructures. This review focuses on the presentation and discussion of single molecules, supramolecular assemblies, and other nanostructures; all research results obtained in our laboratory. The emphasis is directed to the observation of new effects, where the properties of matter at the nanoscale differ from those at the mesoscopic or macroscopic scale: small is different. This fact is illustrated for the conservation of chirality in a hierarchical supramolecular assembly of organic molecules and for local light emission from supported molecules. The latter indicates a possible route towards an optical spectroscopic analysis on the scale of single molecules.