Supported Pd is an essential component for automobile three-way catalyst (TWC). Recent improvement of fuel economy in automobiles requires promotion of catalytic activity of TWC at lower temperatures, especially for combustion of CO and unburned hydrocarbons. In order to obtain a strategy for catalyst design of supported Pd catalysts for low temperature combustion, the essential factors in catalytic activity affected by supports and oxidation states of Pd are summarized in this short review. The following factors are discussed: oxidation states of Pd, effect of substrates and reaction temperature, Pd dispersion, and oxygen storage-release property of supports. The reducibility of Pd species and oxygen storage-release property of supports are emphasized as essential factors for low temperature combustion over supported Pd catalysts.