The combustion research in porous medium burners has been reviewed from the early development in 1912 up to date. A collection of documented works by different authors was classified and their specific interests were addressed. These interests included the evolution and earlier work on the excess enthalpy flame in solid porous medium burners, the analytical treatment, and experimental study of flame stability in such burners. The characterization of the porous burner performance with respect to the relevant parameters was also recorded for both numerical and experimental works. The features of innovative geometries and turbulent flow conditions were demonstrated. The extension of the porous burner operation to incorporate liquid fuel combustion was also included in the classification. Relevant comments and recommendations for future work were attached at the end of each section.