Basic application concepts of catalytic combustion are roughly classified into three types, and the development of catalysts, combustion performance and applicability are stated. On the diffusive catalytic combustion method, completeness of methane combustion and its reaction mechanism have been demonstrated by detailed combustion analysis of the burner and reaction kinetics. On the adiabatic lean premixed catalytic combustion method, applicability of a high-temperature catalyst system based on Mn-substituted hexaaluminate monolithic honeycomb to a 1.5 MW gas turbine combustor has been investigated through pressurized combustion tests and prototype engine-rig tests. As a result, a good outlook of the basic technical problems to overcome including the catalyst durability and the combustor control method was obtained, but another problem was that of the combustor capacity. In view of the progress of the non-catalytic lean premixed combustion method, it was concluded that a hybrid catalytic combustion method limiting catalytic combustion to the low-temperature range in this concept might become efficient in the future, but that it would depend on the development of efficient catalysts initiating their activity at about 350 degrees C and having durability at 1000 degrees C.