We present a systematic theoretical investigation of the surface properties, stability and reactivity, of rock- salt type alkaline-earth metal oxides including MgO, CaO, SrO, and BaO. The accuracy of commonly used exchange-correlation density functionals (LDA, PBE, RPBE, PBEsol, BEEF-vdW and hybrid HSE) and random-phase approximation (RPA) is evaluated and compared to existing experimental values. Calculated surface energies of the four most stable surface facets under vacuum conditions: the (100) surface, the metal and oxygen terminated octopolar (111), and the (110) surfaces exhibit a monotonic increase in stability from MgO to BaO. On the MgO(100) surface, adsorption of CO, NO, CH4 is characterized by physisorption while H2O chemisorbs, which is in agreement with experimental findings. We further use the on-top metal adsorp- tion of CO and NO molecules to map out the surface energetics of each alkaline-earth metal oxide surface. The considered functionals all qualitatively predict similar adsorption energy trends. The ordering between the adsorption energies on different surface facets can be attributed to differences in the local geometrical surface structure and the electronic structure of the metal constituent of the alkaline-earth metal oxide. The striking observation that CO adsorption strength is weaker than NO adsorption on the (100) terraces as the period of the alkaline-earth metal in the oxide increases, is analyzed in detail in terms of charge redistribution within the σ and π channels of adsorbates. Finally, we also present oxygen adsorption and oxygen vacancy formation energies in these oxide systems.