Combustion in inert, catalytic and combustible porous media occurs under the influence of a large range of geometric length scales, thermophysical and thermochemical properties, and flow, heat and mass transfer conditions. As a result, a large range of phenomenological length and time scales control the extent of departure from local thermal and chemical nonequilibrium. The use of intraphase and interphase nonequilibria 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. Improvement of current and design of yet newer and more innovative systems requires further investigations into the gas-phase and surface chemistry, solid-state and condensed-phase physics, transport in disordered structures, and mathematical and numerical methods. Here we summarize the processes leading to thermal and chemical nonequilibrium, their role in the combustion in porous media, their innovative uses and effects on applications, the current modeling of these processes and the modeling techniques that may allow for further improvements and developments.