Applications of synchrotron radiation in physics, chemistry, materials science, and biology has now matured from an exotic experimental field into a well-established area of science. The spectroscopy of molecules and molecular adsorbates on surfaces is one area of science, where, in the past, synchrotron-radiation-related studies had made an impact on understanding the ground-state properties as well as the dynamics. With the new high-brightness synchrotron-radiation sources ahead, this will certainly continue to be a field of very active research. This quasi-monograph reviews the current state of the field for both, the active research scientist, and the new graduate student wishing to become acquainted with this field of research.