Publisher Summary Experimental facts and theoretical concepts, existing in the literature, indicate that the formation of free radicals play an important role in a number of catalytic oxidation reactions. This chapter discusses several studies analyzing the contribution of free radicals to several oxidative transformations of lower alkanes over oxide catalysts. It has been showed that the formation of free radicals in the interaction of alkane molecules with the surface of oxides may prove to be energetically preferable, as compared to any other mechanisms of their activation. The fractions of radicals transformed into different final products depend on the reaction conditions (temperature and oxygen pressure) and on the number of carbon atoms in the alkane molecule. The fate of radicals captured by the surface sites with the formation of the alkoxy groups depends on the number of carbon atoms in the alkane molecule, as well as on the properties of the catalyst surface. The most energetically favorable process of lower alkanes activation over oxide catalysts is a homolytic C–H bond dissociation with the formation of free radicals. The difference in energy expenditures for the formation of free alkyl radicals causes the difference in reactivities between C1–C4 alkanes. The main factors determining the efficiency of different oxides, as catalysts for lower alkanes oxidation, are the H-atom affinity of strong oxidizing surface sites and the oxygen binding energy. These thermochemical factors cause the rates and directions of free-radical reactions and, as a result, the catalytic activity and selectivity to certain products.