Recent work on band structure calculations shows that the Green's function method (KKR) is appropriate not only for metals but also for semiconductors such as selenium, tellurium, and zinc sulphide. The method belongs to the so called « first-principle » methods, in contrast to the interpolation schemes (based e. g. on a pseudopotential). Distinguishing features are its mathematical rigor and rapid convergence. The only shortcoming is that the method only applies to a muffin-tin potential. But since the bands do not depend strongly on the special form of the assumed potential, one should expect reliable results if the real potential is not very far from spherical symmetry. The energy bands calculated for Se, Te, and cubic ZnS fit experiments satisfactorily and are comparable with pseudopotential results. Moreover they are even better than those obtained by tight-binding calculations. That is very promising since there is only one fitting parameter, against e. g. six in the interpolation scheme used in the work on ZnS. Therefore KKR-calculations are an excellent starting point for energy band analysis specially since they require few experimental data. A recent modification of the Green's function method includes spin-orbit coupling from the very beginning.