The most precise atomic mass measurements in Penning traps

•We review the most precise measurements of atomic masses of stable isotopes.•We present the main motivations, methods and results.•Motivations include determining the fine structure constant and neutrino mass.•Methods include image charge detection of single ions in a cryogenic Penning trap.

A perspective is given of the motivations, methods and status of Penning trap atomic mass measurements of long-lived isotopes, with fractional uncertainties near and below 10−10.

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