Geomagnetic pulsations are the ground manifestation of ultra low frequency hydromagnetic waves propagating in the magnetosphere. Frequencies typically range between f  mHz and f  Hz; ground amplitudes range from less than . nT to tens or hundreds of nT and generally increase with latitude up to auroral/cusp regions. The distinct periodicity of most events suggests an interpretation in terms of standing waves reflecting between ionospheres of opposite hemispheres and hydromagnetic resonance is the basic process to interpret most aspects of geomagnetic pulsations. The Kelvin–Helmholtz instability at the magnetopause is considered an important energy source for continuous low frequency events ( f  – mHz); an additional contribution might come from cavity/waveguide modes of the magnetosphere. “Upstream waves” generated by particles reflected from the bow shock along interplanetary magnetic field lines are important exogenic sources for pulsations in the mid-frequency band ( f  – mHz). High frequency pulsations ( f . –  Hz) are traveling waves related to ion-cyclotron instabilities occurring within the magnetosphere. Irregular pulsations represent transient signals associated with dramatic changes of the state of the magnetosphere, related to substorm manifestations. The identification of field line resonance processes represents an important tool for several aspects of magnetospheric diagnostics: a quantitative determination of the set of field line eigenfrequencies can be used to model the plasma distribution along the magnetospheric field lines from equatorial to high latitudes, to monitor temporal variations of the magnetospheric plasma concentration and to highlight interesting aspects of plasmasphere/ionosphere coupling.