Recent decades have seen increased melting of the Greenland ice sheet. On 11 July 2012, nearly the entire surface of the ice sheet melted; such rare events last occurred in 1889 and, prior to that, during the Medieval Climate Anomaly. Studies of the 2012 event associated the presence of a thin, warm elevated liquid cloud layer with surface temperatures rising above the melting point at Summit Station, some 3212 m above sea level. Here we explore other potential factors in July 2012 associated with this unusual melting. These include (1) warm air originating from a record North American heat wave, (2) transitions in the Arctic Oscillation, (3) transport of water vapor via an Atmospheric River over the Atlantic to Greenland, and (4) the presence of warm ocean waters south of Greenland. For the 1889 episode, the Twentieth Century Reanalysis and historical records showed similar factors at work. However, markers of biomass burning were evident in ice cores from 1889 which may reflect another possible factor in these rare events. We suggest that extreme Greenland summer melt episodes, such as those recorded recently and in the late Holocene, could have involved a similar combination of slow climate processes, including prolonged North American droughts/heat waves and North Atlantic warm oceanic temperature anomalies, together with fast processes, such as excursions of the Arctic Oscillation, and transport of warm, humid air in Atmospheric Rivers to Greenland. It is the fast processes that underlie the rarity of such events and influence their predictability.