  The accurate determination of atomic masses and the high-precision
measurement of the bound-electron g factor are prerequisites for the
determination of the electron mass, which is one of the fundamental constants
of nature. In the 2002 CODATA adjustment [P. J. Mohr and B. N. Taylor, Rev.
Mod. Phys. 77, 1 (2005)], the values of the electron mass and the
electron-proton mass ratio are mainly based on g factor measurements in
combination with atomic mass measurements. In this paper, we briefly discuss
the prospects for obtaining other fundamental information from bound-electron g
factor measurements, we present some details of a recent investigation of
two-loop binding corrections to the g factor, and we also investigate the
radiative corrections in the limit of highly excited Rydberg S states with a
long lifetime, where the g factor might be explored using a double resonance
experiment.
