A theoretical study of combustion in porous media driven by a gravity induced gas flux is conducted. Filtration of the oxidizer carrying gas arises in response to heating of the gas due to exothermic conversion of the solid fuel. Specifically, we consider a reaction front propagating through a porous matrix consisting of reactive (fuel) and inert components. Gas, consisting of both oxidizer and inert components, filters through the matrix and reacts with the solid fuel. The hot gases in the medium rise due to buoyancy, thus drawing in Fresh gas from below. Pie employ approximate analytical methods and numerical simulations to analyze all the basic combustion phenomena, including self ignition, external ignition, both upward and downward as well as adiabatic and nonadiabatic propagating combustion waves. Our simulations also describe the dynamics of buoyancy driven combustion waves. In conventional combustion systems the combustion waves are traveling waves, whose wave characteristics, e.g., propagation velocity and shape, are constant, and the time and length scales for the ignition period are independent of the length L of the sample. In contrast, here the waves are not traveling waves. Rather, they are quasisteady waves, whose characteristics do depend on L. Thus, knowledge of the combustion characteristics determined From experiments on a specific sample of a given size can not be generalized to samples of larger size as is the case in conventional combustion. We derive estimates for the dependence of various combustion characteristics on L. Finally, suggestions for the experimental verification of some of the qualitative results of our analysis are presented.