One of the most challenging topics in heterogeneous catalysis is conversion of CH₄ to higher hydrocarbons. Direct conversion of CH₄ to ethylene can be achieved via the oxidative coupling of methane (OCM) reaction. Despite studies which have shown MgO to activate CH₄ and initiate the OCM reaction, its large-scale applications face a significant impediment due to formation of a byproduct, CO₂, and poisoning of the catalyst due to carbonate formation. In the present work, we address two aspects of the OCM reaction on MgO surfaces: carbonate formation on the surface of the catalyst, and (dissociative) adsorption of CH₄. We use first-principles density functional theoretical calculations to determine the energetics and underlying mechanisms of interaction of CO₂ and CH₄ with various surfaces of MgO: (100), (110), and (111) (both Mg- and O-terminations), and the seldom studied, hydroxylated (111) MgO surface with O-termination. We find that the strength of the interaction of CO₂ with MgO surfaces depends on several factors: their surface energies, coordination number of surface O atoms, and ability to donate electrons. However, the O-terminated (111) surface of MgO bucks all aforementioned factors, with only oxygen richness affecting its reactivity towards CO₂. The interaction of CH₄ with MgO surfaces depends primarily on the coordination number of the surface O atoms and the orientation of the CH₄ molecule with respect to the surface. Finally, we provide insights into (a) formation of surface carbonates, which is relevant to CO₂ capture and conversion, and (b) C–H bond activation on MgO surfaces, which is crucial for direct conversion of CH₄ to value-added chemicals.