After touching the history of polyoxometalate (POM) chemistry, the basics of isopolyoxometalates (IPOM) and heteropolyoxometalates (HPOM) are discussed. The main focus is placed on molybdenum- and tungsten-containing IPOM and HPOM. The HPOM are presented based on the coordination of the ‘hetero’atom: tetrahedral (Keggin and Wells–Dawson structures, including their lacunary and mixed anions, Preyssler-Pope-Jeannin polyanion), octahedral (Anderson-Evans structure), square-prismatic (Peacock-Weakley sandwiches) and icosahedral (Dexter-Silverton structure). Subsequently the specifics of polyoxocations (POC) are highlighted, examples of naturally occurring HPOM are given and the nomenclature of POM is discussed. In conclusion, selected applications are presented.