As one increases the heating power in a tokamak beyond a threshold, the confinement undergoes a bifurcation, with a dramatic increase in the confinement time by a factor ~2. This improved confinement regime, or H-mode, is primarily due to the formation of an insulating region at the plasma edge, where steep pressure gradients can form. A feature of H-mode operation is a series of explosive plasma eruptions, called Edge Localised Modes, or ELMs. They repeatedly expel large amounts of energy and particles from the plasma, with serious consequences for the heat loads that plasma facing components must be designed to handle. The present understanding of these ELMs in terms of ideal magneto-hydrodynamic instabilities will be reviewed in this paper.