This thesis addresses the electronic structure of molecules and solids using resonant X-ray emission and photoemission spectroscopy. The use of monochromatic synchrotron radiation and the improved performance of the instrumentation have opened up the possibility of detailed analyses of the response of the electronic systems under interaction with X-rays. The experimental studies are accompanied by numerical ab initio calculations in the formalism of resonant inelastic scattering. The energy selectivity has made it possible for the first time to study how the chemical bonds in a molecule break up during resonant inelastic X-ray scattering. In the conjugated polymer systems, the element selectivity of the X-ray emission process made it possible to probe the different atomic elements separately. The X-ray emission technique proved to be useful for extracting isomeric information, and for measuring the change in the valence levels at different degrees of doping. In this thesis, spectral satellite features in transition metals were thoroughly investigated for various excitation energies around a core-level threshold. By measuring the relative spectral intensity of the satellites it was possible to extract information on the partial core-level widths. Using the nickel metal system as an example, it was shown that it is possible to probe the different core-excited states close toshake-up thresholds by measuring the relative spectral intensity variation of the Auger emission.Resonant photoemission measurements showed unambiguous evidence of interference effects. Theseeffects were also thoroughly probed using angle-dependent measurements. The combination of X-rayemission and absorption were useful for studying buried layers and interfaces due to the appreciable penetration depth of soft X-rays. X-ray scattering was further found to be useful for studying low-energy excited states of rare earth metallic compounds and transition metal oxides.