Résumé
In this review given at the Hot and Cool: Bridging Gaps in Massive Star Evolution conference, I present the state of the art in red supergiant star atmosphere modeling. The last generation of hydrostatic 1D LTE MARCS models publicly released in 2008 have allowed great achievements in the past years, like the calibration of effective temperature scales. I briefly describe this release, and then I discuss in some length the impact of the opacity sampling approximation on the thermal structure of models and on their emergent spectra. I also insist on limitations inherent to these models. Estimates of collisional and radiative timescales for electronic transitions in, e.g., TiO suggest that non-LTE effects are important, and should be further investigated. Also, classical 1D models are not capable of representing the large and non-gaussian velocity fields we know exist in red supergiant (RSG) atmospheres. I therefore summarize current developments in 3D radiative hydrodynamical simulation of RSGs. I show that observed line profiles and shifts are well predicted by these simulations, without the need for arbitrary micro- and macroturbulence velocities. This is great progress, although model line depths and widths are slightly too shallow. These discrepancies are probably caused by the simplified gray radiative transfer used in these computationally demanding simulations. Future non-grey 3D simulations should provide a better fit to observations in terms of line strengths and widths.