The stabilisation of plasma macroscopic instabilities by high energy particles is shown to be a consequence of the conservation of the third adiabatic invariant, i.e. the magnetic flux encircled by the precessional drift orbits. The author discusses the stabilisation mechanism, the physical processes that determine the boundaries of the stable regime, and a comparison between theory and experiment. Considerable progress on the understanding of the fast ion suppression of thermal plasma 'sawtooth' relaxation oscillations has resulted from a profitable interaction between theory and experiments.