Résumé
I review the current status of cool O-rich giant star spectral modelling, stressing some specific problems like line profiles and molecular data completeness. I discuss recent progress in molecular line lists (TiO, VO) and describe recent attempts in modelling normal M-giants as well as AGB star spectra, using static and hydrodynamic models. I anticipate further advances in the near future, with better radiative transfer in hydrodynamic models, that will allow detailed comparisons of models and observations, opening the possibility of deriving stellar parameters from spectroscopic and interferometric observations.