Veniaminof Volcano on the Alaska Peninsula of southwest Alaska is one of a small group of ice-clad volcanoes globally that erupts lava flows in the presence of glacier ice. Here, we describe the nature of lava-ice-snow interactions that have occurred during historical eruptions of the volcano since 1944. Lava flows with total volumes on the order of 0.006 km³ have been erupted in 1983–1984, 1993–1994, 2013, and 2018. Smaller amounts of lava (1 × 10⁻⁴ km³ or less) were generated during eruptions in 1944 and 2021. All known historical eruptions have occurred at a 300-m-high cinder cone (informally named cone A) within the 8 × 10-km-diameter ice-filled caldera that characterizes Veniaminof Volcano. Supraglacial lava flows erupted at cone A, resulted in minor amounts of melting and did not lead to any significant outflows of water in nearby drainages. Subglacial effusion of lava in 1983–1984, 2021 and possibly in 1944 and 1993–1994 resulted in more significant melting including a partially water-filled melt pit, about 0.8 km² in area, that developed during the 1983–1984 eruption. The 1983–1984 event created an impression that meltwater floods from Mount Veniaminof’s ice-filled caldera could be significant and hazardous given the large amount of glacier ice resident within the caldera (ice volume about 8 km³). To date, no evidence supporting catastrophic outflow of meltwater from lava-ice interactions at cone A has been found. Analysis of imagery from the 1983–1984 eruption shows that the initial phase erupted englacial lavas that melted ice/snow/firn from below, producing surface subsidence outward from the cone with no discernable surface connection to the summit vent on cone A. This also happened during the 2021 eruption, and possibly during the 1993–1994 eruption although meltwater lakes did not form during these events. Thus, historical eruptions at Veniaminof Volcano appear to have two different modes of effusive eruptive behavior, where lava reaches the ice subglacially from flank vents, or where lava flows are erupted subaerially from vents near the summit of cone A and flow down the cone on to the ice surface. When placed in the context of global lava-ice eruptions, in cases where lava flows melt the ice from the surface downward, the main hazards are from localized phreatic explosions as opposed to potential flood/lahar hazards. However, when lava effusion/emplacement occurs beneath the ice surface, melting is more rapid and can produce lakes whose drainage could plausibly produce localized floods and lahars.