The oxy-fuel combustion of fossil fuels is a promising carbon capture technology for the design of new thermal power plants as well as retrofitting existing ones to reduce the emission of anthropogenic produced carbon dioxide into the atmosphere. The substitution of air with pure oxygen as the oxidizer and the recirculation of flue gas into the furnace lead to higher amounts of carbon dioxide and water vapor within the combustion chamber compared to air-firing systems, and, thus, strongly impact the thermal radiation by the gas phase. Especially, the erratic behavior of the absorption coefficients of these molecules in the infrared spectral range necessitates the use of a non-gray gas radiation model to accurately predict the radiative heat transfer in oxy-fuel combustion processes by means of numerical solution procedures. In this thesis, the statistical narrow-band and the narrow-band correlated-k models are used to provide the benchmark solutions for the assessment of various radiation models. The accuracy of wide-band and global models is investigated for three different geometries. The parameters of the wide-band models are based on the older spectroscopic database of the exponential wide-band model as well as the newer HITEMP 2010 spectroscopic database. The full-spectrum correlated-k and the weighted-sum-of-gray-gases models are considered to evaluate the performance of global radiation models. For the latter one, seven different parameter sets, derived for air and oxy-fuel conditions, are investigated to provide a recommendation for its possible application in commercially available CFD software. The first two 3D geometries represent a virtual gas turbine combustor with dry oxy-fuel combustion and a virtual furnace of a coal-fired power plant with air-firing, dry and wet oxy-fuel combustion conditions, respectively. Here, it was found that the accuracy of the NBCK model is sufficient to compute reference solutions with less computational effort. For short path lengths at high absolute pressures, all considered gas radiation models show similar accuracy. For long path lengths at atmospheric pressure, the considered pressure path lengths and the spectroscopic database used for the derivation of the radiative properties have a major influence on the accuracy of the simulation results. Here, the FSCK model and the WSGG model with the parameters of Bordbar et al. (2014), both based on the HITEMP 2010 spectroscopic database, are appropriate for modelling the gas radiation. The investigation of various approximations to model the radiative heat transfer in a gas-particulate mixture revealed that gas radiation can contribute up to 50% of the total radiation. Especially, the consideration of gas absorption in regions with lower temperatures is important to compute accurate radiative heat transfer. The approximation of particle scattering as strongly forward scattering via simpler models like Henyey-Greenstein function is sufficient to attain simulation results similar to the benchmark solutions, which were obtained with Mie theory. The application of gray Henyey-Greenstein phase functions obtained with Planck-mean weighted asymmetry factors showed a high accuracy with relative errors less than 10% in comparison to the benchmark solutions. The reduction of the spectral resolution of the radiative properties through applying a wide-band correlated-k or a full-spectrum correlated-k methodology, both based on the HITEMP 2010 spectroscopic database, yield a strong reduction in computational effort with almost no loss of accuracy. In summary, the full-spectrum correlated-k model with the mixture scheme of Modest and Riazzi (2005) in conjunction with gray particle properties is recommended for the use in numerical simulations of real oxy-fuel combustion applications due to its consistently high accuracy and reasonable computational expense for all considered oxy-fuel combustion scenarios.