  Theoretical predictions underlying determinations of the fine structure
constant alpha and the electron-to-proton mass ratio m_e/m_p 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(alpha (Z alpha)^5) and
O(alpha^2 (Z alpha)^5) corrections to the g factor is presented. The
reevaluation of analogous corrections to the Lamb shift and the hyperfine
splitting is summarized.
