With the advent of the very intense 3rd generation synchrotron sources of X rays, new powerful spectroscopic techniques, requiring the detection of very low cross section phenomena, have come of age. Among them Resonant Inelastic X-Ray Scattering (RIXS) is rapidly becoming a major probe of the electronic structure of solids. RIXS measures the decay radiation that follows the excitation of core electrons into states located in a narrow region above the Fermi level. It shares with other core-level spectroscopies a remarkable chemical sensitivity and provides specific information on selected elements in a compound. Since photons are used to excite the process and photons are detected, truly bulk-sensitive information can be obtained. RIXS is sensitive to the nature of the ground state and of the characteristic excitations of a material, and can separately measure their energies, because exciting atoms with different atomic configuration leaves the solid in final states of different total energy. Therefore, it can discriminate different chemical environments and valence states of the same element. In this paper, we outline the basic principles of RIXS, with special emphasis on electronic excitations, and discuss the relevance of this information for studies of hybridization and valence in materials science, by referring to recent experiments.