Combustion in porous media takes advantage of a large range of geometric and phenomenological length scales. These have allowed for the design of new combustion processes and systems, such as, catalytic reactors and converters, porous radiant burners, direct energy and gas conversion devices and systems, chemical sensors, and material synthesis processes. The improvement of the current and the design of yet newer and more innovative systems require further investigations into the gas-phase and surface chemistry, solid-state and condensed-phase physics, transport in disordered structures, and mathematical and numerical methods. This will allow for the development of a new generation of materials, devices, equipments and synthesis processes. Here, we summarize some new and innovative uses of porous media in combustion, the current understanding and modeling of these processes, and the modeling techniques that may allow for further improvements and development.