This is a study of filtration combustion (FC) of rich and ultrarich methane-air mixtures with equivalence ratios between 1 and 4. Particular attention is given to the superadiabatic combustion of ultrarich mixtures where the overall process can be characterized as combustion-based fuel modification and chemical synthesis. In these experiments, essentially one-dimensional FC waves are studied. Temperature profiles and combustion wave velocities as well as chemical composition of the products are determined. In contrast with the ultralean case, which results in complete burnout of the hydrocarbon fuel with formation of carbon dioxide and water, in the rich wave fuel is only partly oxidized in the filtration wave; consequently, the chemical kinetics, heat release, and heat transfer are strongly coupled. The superadiabatic (excess enthalpy) combustion in the ultrarich region has potential for such applications as fuel reforming and synthesis. Preliminary studies have shown the viability of ultrarich filtration combustion for hydrogen production; significant conversion of methane to hydrogen (up to 70%) has been achieved in excess enthalpy porous burners. The present studies include the effect of equivalence ratio on the combustion wave velocity, the combustion temperature, and the composition of the combustion products; the influences of the filtration velocity and the characteristics (chemical composition and pore size) of the ceramic materials on the combustion wave structure and products; and the effects of pressure on the ultrarich waves.