Magnetic moment of a bound electron

Theoretical predictions underlying determinations of the fine structure constant α and the electron-to-proton mass ratio m/m are reviewed, with the emphasis on the bound electron magnetic anomaly g-2. The theory of the interaction of hydrogen-like ions with a magnetic field is discussed. The status of efforts aimed at the determination of O(α() and O(α() corrections to the g factor is presented. The reevaluation of analogous corrections to the Lamb shift and the hyperfine splitting is summarized.