In the field of carbon-free heat generation, there is a growing interest in the design of compact and long-lifehigh-temperature energy systems (HTES) such as gas-to-gas heat exchangers, volumetric solar receivers and radiant tube inserts, among others. They are mostly based on open porous ceramics or reticulated porous ceramics (porosity ~75-95%, cell size ~0.1-10 mm) which can be described as a continuous ligament network delimiting cells in which a fluid can flow. When silicon carbide (SiC) is used as the constitutive material, the whole 3D architecture exhibits outstanding properties such as high thermal shock resistance and high resistance to chemical corrosion in addition to the well-known properties like high specific surface area and good flow-mixing capacity imposed by the associated 3D geometry. The rapid development of additive manufacturing (AM) processes extends furthermore the possibilities to elaborate and manufacture a large range of 3D geometries going from regular lattice structures with different types of unit cells, triply periodic minimal surface-based structures up to more classical irregular strut-based structures. From a thermal modelling viewpoint, one of the main challenges is to take accurately into account thermal radiation in the heat balance of HTES at both transient and steady state states. Even if the contribution of thermal radiation has been highlighted in open-cellfoams 10 years ago (Tseng et al, J. Am. Ceram. Soc.,95[6] 2015–2021 (2012)), engineers and researchers from ceramic science often pay limited attention to it in their everyday practice. This leads to the misuse of these ceramics, which is the source of mechanical damage. To cope with this issue, two main routes of numerical modelling can be used to determine the temperature and/or heat flux fields within 3D structures. The first class of methods, at the continuous macroscopic scale, requires to rigorously solve the radiative transfer equation as long as the studied ceramics follow a Beerian behaviour – namely, when the extinction of the thermal radiation is characterised by an exponential function of the optical thickness. This integro-differential equation can be simplified into an equivalent – but approximate – heat conduction equation by respecting the appropriate hypothesis giving the Rosseland conductivity. However, recent regular 3D architectures obtained by AM processes clearly exhibit a non-Beerian behaviour that leads to investigate other class of methods at the discrete mesoscopic scale. The concept consists in treating the elementary heat exchanges at the ligament scale by using a representative 3D image of the ceramic, beforehand obtained by X-ray µ-tomography or numerical generation. These numerical methods have been recently developed by several French research teams, gathered in the French CNRS research network “GDR TAMARYS” : stabilized vectorial Finite Element schemes, cell-centred Finite Volume models with ray tracing, hybrid Monte Carlo schemes combining motion of Brownian walkers in the solid opaque phase and ray tracing in the fluid phase, and other Monte-Carlo strategies based on integral formulations. This highlight conference will propose a review of the macroscopic and discrete scale approaches for dealing with thermal radiation within conventional and additively manufactured ceramics. As a future work,initiated in the GDR TAMARYS, a federative exercise consisting in the comparison of the different numerical methodologies developed for discrete scale computations will be presented.