Planetary magnetospheres are natural laboratories for many interesting plas
ma physical processes which are difficult to study under normal laboratory
conditions. Among the major processes occurring in space plasmas are the re
connection phenomenon and field line resonances. This paper deals with the
second of these processes. A field line resonance is the resonant coupling
between an isotropic mode and an anisotropic mode in a magnetized plasma. F
ield line resonances allow us to understand many features of ultra-low freq
uency oscillations in the terrestrial magnetosphere, that is resonant mode
coupling is the current paradigm to explain geomagnetic pulsations. A brief
historical introduction as well as a physical description of the field lin
e resonance is given. Resonant mode coupling is discussed for the terrestri
al, Hermean (Mercury), and Kronian (Saturn) magnetospheres, which represent
natural laboratories with different conditions such as size of the laborat
ory, the background plasma density and composition, and the strength of the
magnetic field. This comparative approach allows a deeper insight into the
critical coupling problem than an isolated study of the terrestrial field
line resonance phenomenon. Finally, resonant mode coupling between elastic
wave modes in the solid Earth is briefly tackled and compared with the magn
etospheric situation.