In this paper, attention is focused on adiabatic lean-premixed catalytic combustion, which has attracted interest in the last decades as an environmentally friendly and cost-effective alternative to flame combustion for power generation by gas turbines. The different configurations of the combustion systems for gas turbines are presented. and the results of pilot tests, full-scale bench tests and field trials with retrofitted machines are illustrated. The relevant physico-chemical and catalytic properties of highly active supported PdO catalysts, including reversible PdO-Pd transformation and low-temperature activity, are then addressed. The structural and catalytic properties of highly stable metal substituted hexaaluminates are also discussed. The use of fuel alternative to natural gas is briefly covered. The relevant features of mathematical models for both, the catalyst section and the homogeneous section, that can be used in the design and analysis of the catalytic combustor, are described and the major conclusions of the modelling activity are outlined. Finally, the research opportunities in the area are discussed.