Jökulhlaups, or glacier outburst floods, have occurred during the Holocene from the northern margin of the Vatnajökull ice cap, Iceland. Relatively little is known about the origin, magnitude and frequency of these jökulhlaups. The volcanic rifting zone of northern Iceland provides a new environment in which to examine jökulhlaups. Jökulhlaup reconstructions have to date omitted 2D hydrodynamic modelling techniques. This research therefore reconstructs jökulhlaups from Kverkfjöll volcano, a discrete source of meltwater from northern Vatnajökull. This research describes a suite of erosional and depositional landforms that distinguish Kverkfjöll jökulhlaup routeways. Some of these; clinker-scoured lava, gorges with walls of pillow and subaerial lava, lava steps, cataract-fill mounds and imbricated boulder clusters and run-ups, are previously undocumented jökulhlaup impacts. These landforms may be diagnostic of volcanic and/or rifting landscape jökulhlaups. Cross-cutting relationships and sedimentary stratigraphy suggest at least three Holocene jökulhlaups from Kverkfjöll. Kverkfjöll jökulhlaups were reconstructed using palaeocompetence, slope-area and 2D hydrodynamic modelling. Jökulhlaups were volcanically triggered, had linearly-rising hydrographs and peak discharges of 50,000-100,000 m3s-1, which attenuated by ~75% within 25km. Flows were highly varied spatially and temporally, and strongly controlled by topography, geology and sediment supply. Frontal flow velocities were ~2ms-1 but as stage increased, mean velocities reached 5-15ms-1. Shear stress and stream power reached 1x104 Nm-2 and 1x105 Wm-2 respectively. Flows were initially hyperconcentrated and subsequently more fluidal, supercritical and highly turbulent. Kverkfjöll jökulhlaups achieved geomorphic work comparable to that generated by the largest known terrestrial floods. Landscaping resulted from topographic confinement, steep channel gradients, high hydraulic roughness and an initially abundant but rapidly depleted supply of volcaniclastic sediment. These controls on, and impacts of, jökulhlaups are important for distinguishing high-magnitude water-sediment inputs to the North Atlantic, for recognising jökulhlaups in the rock record and for flood hazard mitigation in similar landscapes and upon glaciated volcanoes.