Stars in the age of micro-arc-second astrometry

The understanding and modeling of the structure and evolution of stars is based on statistical physics as well as on hydrodynamics. Today, a precise identification and proper description of the physical processes at work in stellar interiors are still lacking (one key point being that of transport processes) while the comparison of real stars to model predictions, which implies conversions from the theoretical space to the observational one, suffers from uncertainties in model atmospheres. That results in uncertainties on the prediction of stellar properties needed for galactic studies or cosmology (as stellar ages and masses). In the next decade, progress is expected from the theoretical, experimental and observational sides. I illustrate some of the problems we are faced with when modeling stars and the possible tracks towards their solutions. I discuss how future observational ground-based or spatial programs (in particular those dedicated to micro-arc-second astrometry, asteroseismology and interferometry) will provide precise determinations of the stellar parameters and contribute to a better knowledge of stellar interiors and atmospheres in a wide range of stellar masses, chemical compositions and evolution stages.