The 1982 and 2015 eruptions were the first at Wolf volcano, Galápagos Archipelago, with eyewitness accounts and satellite imagery. Both eruptions were characterized by a rapid and intense initial phase, with multiple eruptive vents, leading to the formation of large ?a?=a lava fields and scarce p=ahoehoe mostly associated with the waning phases. The 1982 eruption started on 28 August from an intra-caldera vent that produced high lava fountains, as well as a radial fissure on the SE flank. The whole eruption lasted for at least 9 days and generated \char12652.5E + 6 m3 DRE (dense rock equivalent) of lava. The 2015 eruption started on 25 May from a circumferential fissure that produced high lava fountains and deposited reticulite scoria on the flanks of the volcano. For the first time since the onset of volcano monitoring in Galápagos, we report cryptotephra from the 2015 eruption reaching and depositing in mainland Ecuador, 1400 km away from the source. Lava from the 2015 circumferential vents covered \char12618.5 km2 on the SE and E flanks. On 13 June 2015, the eruption switched to an intra-caldera vent that was active until 30 June, and produced lava flows that covered most of the caldera floor. The 2015 eruption lasted 36 days and produced \char12687E + 6 m3 DRE of lava, making it the fourth largest eruption in Galápagos since the eruption of Sierra Negra in 1979. We use combined ground-based geophysical surveillance, remote sensing, eyewitness accounts, and detailed field work to constrain the eruptive dynamics of this remote volcano. Our approach allows quantification of eruption rates, which are critical for understanding volcanic systems and for hazard assessment. First order rheological calculations permit us to further constrain the eruption dynamics and emplacement of the lava fields.