As the population of the world is growing rapidly, the demand for energy that is clean and efficient is increasing. Combustion is one of the major ways of energy conversion that produces very high amount of pollutant emission, as such the research arena has been taken over by coming up with combustion processes that are cleaner and efficient by the combustion engineers. Flameless combustion is one of the new techniques discovered by researchers to suppress NOx emission due to the low temperature inside the combustion zone that is well below the dissociation temperature of Nitrogen. Homogenous or proper mixing is another major factor that enhances combustion efficiency. An asymmetric swirling combustor is a unique shaped combustor that was developed by researchers in order to enhance better mixing inside the combustion zone without the need for an external swirler. The review investigated several parameters such as temperature uniformity, fuel flexibility and level of pollutant emission as discussed by researchers and it was found that the asymmetric swirling combustor is very efficient with temperature uniformity of about 0.9, thermal efficiency of 53% and very low NOx and CO of about 2ppm and 24ppm according to researchers. It was recommended that the combustor should be investigated under different flow configurations i.e. forward and reverse flow in order to know the optimum direction of flow for the asymmetric swirling combustor.