Catalytic properties of heteropoly compounds as well as their syntheses, structures, and fundamental chemical properties are described. The term heteropoly compounds are used here for heteropolyacids (HPAs) and their derivatives, and these are also called polyoxometalates and metal–oxygen clusters. Since the chemical properties such as acidic and redox properties can be controlled in a wide range by choosing the constituting elements of polyanions and the polyanion structures, these compounds are valuable materials for the design of practical catalysts and also fundamental studies of catalysis. As for the solid HPA catalysts, the hierarchical structure (primary, secondary, and tertiary structures) and the presence of three types of catalyses, (1) surface-type, (2) bulk-type (I) or pseudoliquid, and (3) bulk-type (II)) catalysis, are important for understanding the catalysis of HPA and catalyst design based on HPA.

There are already several industrial processes utilizing these compounds as catalysts for oxidation and acid-catalyzed reactions both in liquid phase and in gas–solid phase. Most widely used HPAs are of Keggin-type, e.g., H₃PMo₁₂O₄₀ and H₃PW₁₂O₄₀. In addition, the promising future opportunities of HPA catalysts such as bifunctional catalysts like a combination of HPA with noble metal, hydrophobic HPA catalysts, shape-selective HPA catalysts, and HPA having novel polyanion structures and compositions are described.