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The magnetic moment (g‐factor) of the electron is a fundamental quantity in physics that can be measured with high accuracy by spectroscopy in Penning traps. Its value has been predicted by theory, both for the case of the free (unbound) electron and for the electron bound in a highly charged ion. Precision measurements of the electron magnetic moment yield a stringent test of these predictions and can in turn be used for a determination of fundamental constants such as the fine structure constant or the atomic mass of the electron. For the bound‐electron magnetic‐moment measurement, two complementary approaches exist, one via the so‐called "continuous Stern–Gerlach effect", applied to ions with zero‐spin nuclei, and one a spectroscopic approach, applied to ions with nonzero nuclear spin. Here, the latter approach is detailed, and an overview of the experiment and its status is given. [ABSTRACT FROM AUTHOR]