Recent developments for catalysis by heteropoly compounds as both acid and oxidation catalysts have been described. The acid strength of typical heteropoly acid, H3PW12O40, was found to be higher than that of H2SO4 in liquid-state and that of H-ZSM-5 in solid-state. The catalytic activity for acid-catalyzed reactions was greatly enhanced by supporting it on mesoporous silica (MCM-41) and the formation of an acidic Cs salt, Cs2.5H0.5PW12O40. The Cs2.5H0.5PW12O40 is hydrophobic and active for "water-tolerant catalysis". Bifunctional catalysts Pt-Cs2.5H0.5PW12O40 and its SiO2-supported catalyst were effective for skeletal isomerization of n-alkanes. Isotopic study using C-13-n-butane revealed that the isomerization of n-butane proceeds mainly via monomolecular mechanism over Pt-Cs2.5H0.5 PW12O40. The Pt-Cs2.1H0.9PW12O40 possessed ultramicropores with the width between 0.43 and 0.50 nm and exhibited shape selectivities for oxidation, hydrogenation, and skeletal isomerization of n-butane. As a typical example for oxidation catalyzed by heteropoly compounds, selective oxidation of methane with hydrogen peroxide has been focussed. The H4PVMo11O40 was found to be very efficient for the reaction. The reaction scheme, active species, and the role of heteropoly anion have been proposed.