In this paper research and development work of the authors is described, which led to the design of a new combustor-heat exchanger system based on the combustion in porous media. Combustion in inert porous media is possible if the Peclet-number is high enough (> 65), so that quenching of the flame inside the pores is prohibited. The heat transfer from the combustion zone, to the porous medium itself is very effective because of the very large surface between them. The combustion temperature can be controlled through the porous medium temperature. Prompt and thermal NOx formation, which is temperature dependent, can be controlled by appropriate cooling of the combustion zone. The heat transfer mechanisms in the combustor are discussed and new designs of porous materials are proposed, which allow a high power density and a better control of the temperature level in the combustion zone. The possible application field and the expected benefits of this combustion technique are discussed.