This work is a comprehensive study of combustion in porous inert media (PIM) with focus on the effects of pressure and air/fuel equivalence ratio. Experiments on lean flame stability limits, flame stabilization and temperature profiles in porous inert media burners of different geometry have been carried out at nearly adiabatic conditions. The experiments were complemented by numerical simulations of combustion in porous inert media, employing a volume-averaged 1D model and 3D direct pore level simulation (3D DPLS) on real geometries of sponge like structures. A definition of the burning velocity is proposed to compare the geometrically different burners investigated. The numerically obtained macroscopic thermal flame thicknesses and the burning velocities are compared with that of free flames. The results show a non-monotonic dependence of the burning velocity on pressure considerably affected by the air/fuel equivalence ratio, which is well depicted by the models used in this work with some identified limitations. By performing a parametric study with the 1D model, dispersion of heat and mass has been identified as the major responsible mechanism of increasing of burning velocity with pressure. The DPLS results showed considerable temperature variations along the space coordinate, which were not considered up to now in 1D models when calculating reaction rates and which could be the reason of the observed limitations. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.