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The determination of the electron mass from Penning-trap measurements with$^{12}$C$^{5+}$ ions and from theoretical results for the bound-electron $g$factor is described in detail. Some recently calculated contributions slightlyshift the extracted mass value. Prospects of a further improvement of theelectron mass are discussed both from the experimental and from the theoreticalpoint of view. Measurements with $^4$He$^+$ ions will enable a consistencycheck of the electron mass value, and in future an improvement of the $^4$Henuclear mass and a determination of the fine-structure constant.

Extraction of the electron mass from $g$ factor measurements on light hydrogenlike ions