The various concepts of catalytic combustion for the production of energy are presented first. Then, the different configurations of catalytic combustion systems for gas turbine applications are described. The following aspects of the mathematical modeling of the catalyst section are addressed: (1) relevant physical and chemical phenomena; (2) comparison of mathematical models; (3) estimation of interphase transfer coefficients; (4) acquisition of kinetic data; (5) continuous versus discrete multichannel models. Selected examples of application of the models are then presented. Finally, the mathematical modeling of the homogeneous section is briefly discussed.