Deflagrations in porous energetic materials are characterized by regions of two-phase flow where significant velocity and temperature differences between the gaseous and condensed phases act to modify the structure and propagation velocity of the combustion wave. In the present work, recent models that describe propagating deflagrations under varying degrees of confinement, as represented by the pressure difference ( or overpressure) between the burned and unburned regions, are reviewed. It is shown how the structure, propagation speed, and final temperature of the combustion wave depend on the porosity and local pressure in the two-phase regions, even in the unconfined limit corresponding to zero overpressures. For the more general confined problem, however, exhibiting the burning-rate response as a function of overpressure is shown to additionally predict the well-known transition from conductive to convective burning associated with the preheating of the unburned material by the burned gases. Inclusion of temperature-nonequilibrium effects serves to further sharpen this transition and ultimately suggests a modified structure for the combustion wave in the convection-dominated regime.