Volcanic eruptions under glaciers can cause dangerous floods and lahars(1-3) and create hyaloclastite (fragmented glassy rock) mountains(4-8), But processes such as the rate of heat transfer between ice and magma, edifice formation, and the response of the surrounding glacier are poorly understood, because of the lack of data. Here we present observations from the fissure eruption at Vatnajokull ice cap, Iceland, in October 1996. In the 13 days of the eruption 3 km(3) of ice were melted and the erupted magma fragmented into glass forming a hyaloclastite ridge 6-7 km long and 200-300 m high under 500-750 m of ice. Meltwater of temperatures of 15-20 degrees C flowed along a narrow channel at the glacier bed into the Grimsvotn subglacial lake for five weeks, before draining in a sudden flood, or jokulhlaup. Subsidence and crevassing of the ice cap occurred over the eruptive fissure and the meltwater path, whereas elsewhere the glacier surface remained intact, suggesting that subglacial eruptions do not trigger widespread basal sliding in warm-based glaciers.