In this paper we review the results of analytical, numerical and experimental studies related to air injection into porous medium containing initially light oil, water and gas at medium pressure conditions. The new combustion mechanism is described, where the process of the medium temperature oxidation interacts with the oil vaporization/condensation, resulting in a resonant combustion wave structure. We discuss bifurcations of combustion regimes with a change of reservoir parameters, and analyze the effectiveness of the proposed technique for recovery in light oil reservoirs.