The synthesis, characterisation, chemistry and uses of a wide arrange of polyhedral silsesquioxanes of the general formula SinO3/2nRn (where R=H, alkyl, aryl, etc., and n=4, 6, 8, 10 etc.) is described. Much of the discussion is centred on the compounds Si8O12R8 which have become important building blocks for a wide range of materials useful in, for example, nanocomposites, dendrimers, and optical materials. The synthesis of POSS molecules can be carried out from monomeric Si-containing precursors or by modification of more complicated siloxanes, these various methods are described. The physical properties and spectroscopic parameters of many POSS compounds are also described together with a review of computational studies on their structures.