We present a general discussion of chemical shifts in core-level photoelectron spectroscopy. There are two different starting points that are commonly used for describing the important ingredients in the chemical shifts. In the first approach one starts out by considering the shifts on the Koopmans level, often using simplified models. This “ground-state” shift may then be modified by relaxation effects. It is, however, often assumed that this contribution to the shift is small. The second model describes more explicitly the shift in terms of differences in the total energy of the initial state prior to ionization and the final core ionized state. It will be argued that the latter description is the only reliable one for many systems. A discussion of what properties of a system determine the chemical shift will be presented for adsorbates, metal surfaces and alloys.