With the increasing evidence of the potential disastrous consequences arising from global warming, there is a need to reduce greenhouse gas emissions, and gas-fired power generation represents an attractive option due to its low carbon intensity. Nevertheless, gas is not a zero-emission fuel and therefore it is necessary to control the emissions associated with its usage. Among the carbon capture techniques suitable for gas-fired generation, postcombustion is regarded as the most feasible in the short-term. The additional costs associated with the CO2 capture process can be reduced by employing modified cycle concepts such as EGR and STIG, which are characterised by a diluted combustion environment. The development of accurate numerical models for the combustion process in industrial devices under diluted conditions can be very useful in assessing the impact of dilution on the combustion process, and represents the main goal of the present work. Firstly, the impact of carbon dioxide and steam dilution on natural gas combustion has been assessed by means of detailed simulations of simple unidimensional laminar ames. It has been found that even the relatively low dilutions levels typical of EGR and STIG cycles have a significant impact on the combustion process. Also, the diluting species participate directly in the combustion chemistry, and therefore there is a need to include detailed chemistry and finite rate-effects in a CFD model for realistic configurations. In this respect, the suitability of the RANS and LES FGM/presumed-PDF approach for the modelling of swirling partially-premixed flames has been assessed. The performance of different turbulence models with different levels of mesh refinement have been assessed against in-ame measurements in a lab-scale burner and guidelines for the CFD modelling of industrial devices have been inferred. Finally, the previous findings have been employed to develop a complete CFD model for an industrial MGT combustor, which has been investigated under both air-fired and diluted operation. The numerical results have compared with the available experimental data. It has been concluded that the model is able to predict the impact of dilution on the heat release, flame stabilisation, flow-field and pollutant emissions.