The development of low-temperature scanning tunneling microscopes (STM) operating under ultrahigh vacuum conditions has provided new opportunities for investigating locally the electronic and magnetic structure at surfaces. Three examples are chosen from our laboratory, which illustrate the power and the potential of this local approach. (i) Light emission from individual C 60 molecules on a Au(111) surface --an avenue to combine powerful optical techniques with the high lateral resolution of the STM. (ii) Kondo effect of a single magnetic Ce-adatom on Ag(111) --new perspectives for probing magnetic nanostructures. (iii) Two-dimensional self-assembly of supramolecular structures on metal surfaces, a step towards understanding and control of supramolecular aggregation.