Jökulhlaups in Iceland may originate from marginal or subglacial sources of water melted by atmospheric processes, permanent geothermal heat or volcanic eruptions. Glacier-volcano interactions produce meltwater that either drains toward the glacier margin or accumulates in subglacial lakes. Accumulated meltwater drains periodically in jökulhlaups from the subglacial lakes and occasionally during volcanic eruptions. During the 20th century 15 subglacial volcanic eruptions (10 major and 5 minor events) took place, about one-third of all eruptions in Iceland during that century. The release of meltwater from glacial lakes can take place as a result of two different conduit initiation mechanisms and the subsequent drainage from the lake occurs by two different modes. Drainage can begin at pressures lower than the ice overburden in conduits that expand slowly over days or weeks due to melting of the ice walls by frictional and sensible heat in the water. Alternatively, the lake level may rise until the glacier is lifted along the flowpath to make space for the water and water discharges rise linearly, peaking in a time interval of several hours to 1-2 days. In this case, discharge rises faster than can be accommodated by melting of the conduits. The rapidly-rising floods are often associated with large discharges and floods following rapid filling of subglacial lakes during subglacial eruptions or dumping of one marginal lake into another. Jökulhlaups during eruptions in steep ice and snow-covered stratovolcanoes are swift and dangerous and may become lahars and debris-laden floods. Normally jökulhlaups do not lead to glacier surges but eruptions in ice-capped stratovolcanoes have caused rapid and extensive glacier sliding. Jökulhlaups have significant landscaping potential: they erode large canyons and transport and deposit enormous quantities of sediment and icebergs over vast outwash plains and sandur deltas. Jökulhlaups from subglacial lakes may transport on the order of 107 tons of sediment per event but during violent volcanic eruptions the sediment load has been 108 tons. Pleistocene glacial river canyons may have been formed in such catastrophic floods from subglacial lakes. Jökulhlaups have threatened human populations, farms and hydroelectric power plants on glacier-fed rivers. They have damaged cultivated and vegetation areas, disrupted roads on the outwash plains and have even generated flood waves in coastal waters. Iceland is a unique and valuable study-site for glaciovolcanic interactions. This applies to the heat exchange between magma and the glacier, the dynamical response of the glacier to subglacial eruptions, the structure and growth sequence of hyaloclastite ridges and tuyas formed by subglacial eruptions, and jökulhlaups due to volcanic eruptions. The jökuhlaups can be seen as modern analogues of past megafloods on the Earth and their exploration may improve understanding of ice-volcano processes on other planets.