The breathing mode is a low frequency, longitudinal bulk instability observed in a majority of Hall thrusters. Its occurrence is accompanied by wide, regular discharge current oscillations in the 10 - 30 kHz range. A concise outline of the prevailing interpretations of this mode is provided, followed by an overview of a recently proposed theory. It is eventually shown that this ionization instability is not related to the motion of the ionization front but to an ionization predator-prey cycle, the former phenomenon being rather a consequence of the latter.