Methane, discovered in 1766 by Alessandro Volta, is an attractive energy source because of its high heat of combustion per mole of carbon dioxide. However, methane is the most abundant hydrocarbon in the atmosphere and is an important greenhouse gas, with a 21-fold greater relative radiative effectiveness than CO2 on a per-molecule basis. To avoid or limit the formation of pollutants that are dangerous for both human health and the atmospheric environment, the catalytic combustion of methane appears to be one of the most promising alternatives to thermal combustion. Total oxidation of methane, which is environmentally friendly at much lower temperatures, is believed to be an efficient and economically feasible way to eliminate pollutants. This work presents a literature review, a statu quo, on catalytic methane oxidation on transition metal oxide-modified ceria catalysts (MOx/CeO2). Methane was used for this study since it is of great interest as a model compound for understanding the mechanisms of oxidation and catalytic combustion on metal oxides. The objective was to evaluate the conceptual ideas of oxygen vacancy formation through doping to increase the catalytic activity for methane oxidation over CeO2. Oxygen vacancies were created through the formation of solid solutions, and their catalytic activities were compared to the catalytic activity of an undoped CeO2 sample. The reaction conditions, the type of catalysts, the morphology and crystallographic facets exposing the role of oxygen vacancies, the deactivation mechanism, the stability of the catalysts, the reaction mechanism and kinetic characteristics are summarized.