The design, theory and characteristics of combustors in which the reactants (or the combustion air alone) are preheated using heat recycled from beyond the flame zone, without mixing the two streams, are reviewed. There is a great variety of such systems, based on a combustor in between the two limbs of a heat exchanger, ranging from the so called ＇＇self-recuperative＇＇ burners which save a substantial proportion of fuel when used to replace conventional burners in heating up furnaces to a given temperature, over beds of particulates and ＇＇filtration＇＇ combustion, to systems able to burn mixtures normally considered incombustible, which are currently used mostly for incineration. A review of their theory shows that such devices have the potential for very high efficiencies. Their recent application to radiant burners, I.C. engines, and to the pollution-free combustion of lean hydrogen/air mixtures is surveyed.