In the Internal Constitution of the Stars, published in 1926, Eddington gave a central temperature of white dwarfs of several billions degrees. The Fermi-Dirac statistics appeared just one year later, in 1927, and the new equation of state for degenerate matter provided the explanation of white dwarfs.

The solution of the problems we have to consider presently are probably not relevant of the same kind of intellectual jump. But who knows! Anyhow, the time of the perfect gas law is definitely over. It is possible, in many cases, to get astrophysical orders of magnitude, using simple or oversimple relations betwen physical quantities. However, modeling correctly observational results has become, nowaday, more and more difficult. Data are of a better precision and provide more information, would it be chemical abundances, evolutionary tracks or those wonderful helioseismological data. An elementary statement is that, in order to look Inside the Stars (the title of a recent colloquium), we need more accurate descriptions of basic physical laws: equation of state, opacities, thermonuclear reactions.

We are still facing many difficulties in the field, and we can give a few examples: we do not have a theory which decribes consistently both the equation of state of a plasma and the level population of the atoms; we still have to improve the theory of screening effects in dense plasmas; we have now a description of cold, dense, weakly ionized matter of brown dwarfs, but it is still incomplete.