This review article focuses on developing active catalysts for the direct conversion of CH4 to C2H6 and C2H4 by utilizing CO2 as an oxidant. The catalytic effectiveness of a number of unsupported metal oxides in the reaction of CH4 and CO2 is first examined at 850 degrees C under ambient pressure with a fixed-bed quartz reactor. The oxides of Cr, Ce and In show high conversions of CH4 and CO2 of 13-14 mol% and 28-32 mol%, respectively, whereas some lanthanide oxides and CaO exhibit high C-2 selectivity of 48-55 %. It is suggested that redox potential of metal oxide works for activating feed gas and its basic property controls C-2 formation. Among all of the oxides examined, the highest C-2 yields of 1.1-1.4 mol% are observed with Pr and Tb catalysts, where C-2 formation proceeds via a redox cycle involving labile lattice oxygen atoms. In order to improve Ct yield, CeO2 or Cr2O3 with high redox potential is then modified with CaO with strong basicity. The binary catalyst of CaO-CeO2 or CaO-Cr2O3 has remarkable synergistic effect on C-2 formation at 850 degrees C; C-2 yield at Ca/Ce or Ca/Cr ratio of 0.5 is 30 or 70 times that over each component, respectively. As partial pressure of CO2 increases under that of CH4 of 30 kPa, both C-2 yield and C-2 selectivity increase and reach the highest values of 4.0 mol% and 60-70 % at 70 kPa, respectively. The catalytic performance of these binary oxides is stable during 8-10 h reaction. The XRD, XPS, and CO2-TPD measurements suggest that CO2 adsorption on Ca sites and subsequent activation on neighboring Ce or Cr sites produce active oxygen species, which play a key role for selective formation of C-2 hydrocarbons.