Cellular media such as plastic, ceramic and metal foams present specific characteristics that make them interesting for a number of applications related to thermal engineering. Their ability to minimize natural convection makes them ideal candidates for insulation applications, while the high specific surface and permeability to fluid of open cell foams makes them interesting heat transfer enhancers. In addition, their permeability to light makes them an ideal candidate for thermal radiation based applications, such as porous burners or solar energy collectors. In many of these application, thermal radiation heat transfer can have a significant influence on the heat transfer process. Both accurate radiation models and accurate morphological models of the structure of the foam are required. This work provides an original contribution on both these accounts. A discussion of the literature on numerical methods for radiation heat transfer in cellular media is presented, with focus on Monte Carlo methods. Homogeneous Phase (HPA) and Multi Phase (MPA) methods are discussed. Further efforts are required to accurately model and digitally replicate of foam morphologies. Our goal is to digitally generate three commonly occurring types of foam structures, covering a large range of real materials: high-porosity open cell foams, high-porosity closed cell foams, low-porosity open-cell structures. For high-porosity open cell foams, the automated parametric digital generation technique was validated against a dataset consisting of raw morphological data obtained by tomographic analysis. The generation capabilities were then applied to parametrically investigate the influence of morphological parameters on the radiative properties (namely, the extinction coefficient) of an opaque open-cell foam. Highly accurate analytical relationships were subsequently deduced and validated by comparison with results obtained from tomography samples. Modeling radiation in foams with a semi-transparent solid phase is substantially more complex. A Direct Monte-Carlo Homogenization reference technique is proposed, that allows to simulate radiation within arbitrary cavities and calculate macroscopic radiative quantities based on a Representative Elementary Volume (REV) of cellular material. The technique is validated against full scale Monte Carlo simulations. Improvements of the existing Homogeneous Phase and Multi Phase approach are proposed, through extensive use of inverse methods and the addition of one equation to take into account specific phenomena taking place in the semi-transparent solid phase. The resulting Improved Homogenized Approaches are extensively tested by comparing them with Direct Monte Carlo Homogenization simulations and existing homogenized models, on a varied set of morphologies making full use of the previously developed digital generation techniques. The improved models consistently outperform existing homogenized models.