Understanding the stellar interiors is an important issue for astrophysics, but also for fundamental physics. The physical description of the stellar material implies statistical physics as well as hydrodynamics. We give examples of unsolved physical problems and their consequences for predictions of stellar properties and evolution. It is shown that the accumulation of high-quality data like distances and photometry on a large variety of objects, as proposed by GAIA, will be very useful. During the same period, asteroseismology will develop both from the ground in velocimetry, and from space in photometry, providing for the closest stars, a direct insight into their interiors. This ensemble of new data will constitute the basis of the general physical description of stellar interiors.