In response to the need to develop low NOx combustors, there has been renewed interest in catalytic combustion and a new sense of urgency in seeking to overcome the remaining hurdles and develop a commercial unit. Starting with an explanation of how the shape of a ’light-off’ curve for a catalyst may vary, progress in the development of low, medium and high temperature catalyst systems is described. Since gas turbines need to be capable of operating at varying power loads, where the gas inlet conditions vary, hybrid systems have been developed. These are reviewed in this paper and the challenges faced by interdisciplinary teams working on system designs are described. In general, schemes have progressed on the lines of maximizing catalytic reactions until gas temperatures exceed 800 degrees C, at which point homogeneous reactions become significant. Since natural gas is an abundant and relatively clean fuel, it is used in many of the schemes described, and because of pressure drop constraints monoliths are favoured as catalyst support systems. Practical advice is also provided on the use of mathematical modelling techniques which should proceed in parallel with system design, utilizing established knowledge in chemical reaction engineering in order to make progress. An overview of the reactions and transport processes taking place is described, and the difficulties of obtaining kinetic and transport/physical property data are outlined. Despite the considerable progress that has been made, many challenges remain and a number of these centre on system design and how to cope with varying power loads. In addition, issues concerning catalyst durability fuel-air mixing, minimization of stresses, and start-up need attention.