It is now nearly fifty years since Eddington and Milne had a lively controversy on the importance of the surface boundary condition on the internal structure of stars [see Eddington (1930) and Milne (1930)]. We remember that Eddington believed that the internal structure of stars is basically determined by the physical processes occurring in the deep interior and that what happens in the surface layers has little effect on the total stellar luminosity. On the other hand, Milne emphasized the importance of the properties of the outer layers and the effect these could have on the run of pressure and temperature in the deep interior of the stars. We know now that both Eddington and Milne were correct. Eddington’s considerations apply to the hot stars, the early-type stars which have surface layers in radiative equilibrium. Milne’s arguments are relevant to the cool stars, the late-type stars which have deep convective envelopes. In the former case, one can safely assume in calculations of stellar structure that the density and the temperature both approach zero simultaneously at the surface (the so-called “zero” surface boundary conditions).