The results are summarized of studies on energetic ion transport induced by sawtooth oscillations intokamaks. The main attention is paid to a description of the physicalmechanisms responsible for this transport. In addition to an overview, new material is also presented. The new results concern the resonant interaction of the particles and theelectromagnetic field of sawtooth crashes. In particular, itis discovered that the dominant harmonic of the crashes (m = n = 1)can lead to stochastic motion of particles with large orbitwidths (`potato' orbits). The regular motion of potato orbits andquasi-stagnation particles in the presence of an n = 1 mode isstudied, and their characteristic displacements associated withquick switching on and off of the mode are found.