  Recent progress in quantum electrodynamics (QED) calculations of highly
charged ions is reviewed. The theoretical predictions for the binding energies,
the hyperfine splittings, and the g factors are presented and compared with
available experimental data. Special attention is paid to tests of bound-state
QED at strong field regime. Future prospects for tests of QED at the strongest
electric and magnetic fields as well as for determination of the fine structure
constant and the nuclear magnetic moments with heavy ions are discussed.
