Since its introduction, the orbitrap has proven to be a robust mass analyzer that can routinely deliver high resolving power and mass accuracy. Unlike conventional ion traps such as the Paul and Penning traps, the orbitrap uses only electrostatic fields to confine and to analyze injected ion populations. In addition, its relatively low cost, simple design and high space‐charge capacity make it suitable for tackling complex scientific problems in which high performance is required. This review begins with a brief account of the set of inventions that led to the orbitrap, followed by a qualitative description of ion capture, ion motion in the trap and modes of detection. Various orbitrap instruments, including the commercially available linear ion trap–orbitrap hybrid mass spectrometers, are also discussed with emphasis on the different methods used to inject ions into the trap. Figures of merit such as resolving power, mass accuracy, dynamic range and sensitivity of each type of instrument are compared. In addition, experimental techniques that allow mass‐selective manipulation of the motion of confined ions and their potential application in tandem mass spectrometry in the orbitrap are described. Finally, some specific applications are reviewed to illustrate the performance and versatility of the orbitrap mass spectrometers.