Zeeman splitting in highly charged ions: high-precision experiments and bound-state QED

The g factor of low-Z hydrogen-like and lithium-like ions proved to be a sensitive tool for testing bound-state quantum electrodynamics and for the determination of fundamental constants. Moreover, QED effects beyond the Furry picture are accessible in these investigations. Anticipated experiments with boron-like ions will uncover the nonlinear contributions to the Zeeman splitting. Recent experimental and theoretical investigations are reviewed along with possible future developments.