Exact Results in Quantum Theory

Experiments on the bound-electron g factor provide one of the most stingent tests of the bound-state QED. In combination with sophisticated theoretical calculations, these experiments deliver presently the best determination of the electron mass. In my talk, I review the present status of theory and experiment of the g factor of light hydrogen-like and lithium-like ions. Perspectives for the determination of the fine structure constant from a weigthed difference of the g factors of hydrogen-like and lithlium-like ions are discussed.