Low-dimensional systems (LDSs) such as zero-dimensional nanoclusters, one-dimensional atomic or molecular wires, and two-dimensional expanded or condensed overlayers are preferentially formed "delocalized'' at surface inhomogeneities of a foreign substrate (S). A delocalized formation of metal, hydrogen, oxygen, or halide LDSs takes place at undersaturation conditions in electrochemical systems with a strong interaction (binding) energy between adatoms or admolecules and S. Under electrochemical conditions, undersaturation is equivalent to underpotential. In this range, underpotential deposition as well as underpotential dissolution processes of LDSs take place. A "localized'' formation of LDSs on quasi-perfect foreign S surfaces or atomically flat S terraces additionally requires a tip or a cantilever of a scanning probe microscope operating as an electrochemical nanoelectrode. In this case, defined metal or oxide LDSs for nanostructuring of foreign metal and semiconductor surfaces can be formed. This paper deals first with the formation, stability, and dissolution of metal LDSs. Second, the LDS concept is applied to hydrogen, oxygen, and halide LDSs for a better understanding of different phase formation and dissolution processes on an atomic level such as hydrogen and oxygen adsorption on noble metal surfaces, dissolution and passivation of iron group metals, and the breakdown of passivity by halide-induced pitting corrosion.