In Fourier-transform ion cyclotron resonance mass spectrometry, ions are detected by measuring image current induced in the detecting electrodes by trapped ions rotating in a magnetic field at their cyclotron frequencies. The ion trap used for this purpose is called the Penning trap. It can have various configurations of electrodes that are used to create a trapping electric field, to excite cyclotron motion, and to detect the induced signal. The evolution of this type of mass spectrometry is mainly driven by progress in the technology of superconducting magnets and in the constantly improved design of the ion cyclotron resonance (ICR) measuring cell. In this review, we focus on ICR cell designs. We consider that the driving forces of this evolution are the desire to increase resolution, mass accuracy and dynamic range, as well as to adapt new methods for creating and trapping ions. © 2020 Wiley Periodicals LLC.