Polyoxometalates containing noble metal ions, such as ruthenium, osmium, rhodium, palladium, platinum, silver and gold, are a structurally diverse class of compounds. They include both classical heteropolyanions (vanadates, molybdates, tungstates) in which noble metals are present as heteroatoms, as well as the recently discovered class of polyoxometalates with noble metal "addenda" atoms. The focus of this Review is on complexes that should, in principle, exist as discrete molecular species in solution, and which are therefore of interest for their reactivity, their future synthetic utility and potential applications, for example, in catalysis or nanoscience.