This review is devoted to trapping mass spectrometry wherein ions are confined by electromagnetic fields for prolonged periods of time within limited volume, with mass measurement taking place within the same volume. Three major types of trapping mass spectrometers are discussed, specifically radiofrequency ion trap, Fourier transform ion cyclotron resonance and Orbitrap. While these three branches are intricately interwoven with each other over their recent history, they also differ greatly in their fundamentals, roots and historical origin. This diversity is reflected also in the difference of viewpoints from which each of these directions is addressed in this review. Following the theme of the issue, we focus on developments mainly associated with the country of Germany but, at the same time, we use this review as an illustration of the rapidly increasing globalization of science and expanding multi‐national collaborations.