The catalytic reduction of SO2 to elemental sulfur by CO and CH4 over Cu-modified ceria catalysts is studied in this work. Doped and undoped ceria are active catalysts for the SO2 reduction by CO or CH4 in the temperature range 450-750 degrees C. When CO is used as the reductant, the reaction follows the redox mechanism, and formation of surface defects (oxygen vacancies) and ceria reducibility are important for catalyst activity. SO2 strongly adsorbs on the catalyst surface forming sulfates. Partial reduction of sulfate by CO is necessary for the reaction to light off and proceed at low temperatures. Addition of copper improves the low-temperature catalyst activity by increasing the reducibility of ceria and providing sites for CO adsorption. On the other hand, methane activation is limited by the thermal stability of surface sulfates. The activation of methane may involve surface oxygen species and partially reduced metal oxide sites at high temperature. Two independent reactions are proposed and used to explain the catalytic performance of ceria-based oxides in CH4+SO2 gas mixtures. One reaction leads to elemental sulfur and complete oxidation (CO2+H2O) products, while the second produces H2S and CO+H2O under fuel-rich conditions. The addition of copper suppresses the latter, thus increasing the catalyst selectivity to elemental sulfur. The catalyst activity/selectivity studies were complemented by SO2 uptake experiments in a TGA and reduction studies of the as-prepared and pre-sulfated catalysts in CO and methane, both isothermally and in the TPR mode.