Inert porous media are used in advanced combustion devices that are essential to a variety of energy technologies in order to enable the maximum possible power density and power conversion efficiency needed for economic competitiveness and energy conservation with reduction in pollutant emissions. In these and other applications, the desirable characteristics of inert porous media are used to influence the relevant fluid dynamic, thermal, and chemical processes by varying the geometrical and/or physical properties of the porous matrix. In this manner, the flow, the temperature, and the distribution of species concentrations may be controlled. After a brief consideration of the models, the two-energy equation (i.e., local thermal nonequilibrium) model is discussed, and the transport coefficients needed for implementing the model equations to predict premixed combustion in high-porosity porous inert media are briefly reviewed. Despite the fact that some of the fundamental processes taking place in the inert porous media are still not well understood and properties not well known, considerable progress, however, has been made in the numerical modeling of combustion in porous burner-combustors, burner-radiant heaters, and burners-heat exchangers, and these combustion systems are discussed in this paper. Further development of more accurate models and their use in the preliminary design and/or optimization of porous materials-based combustion devices is encouraged.