Present-day volcano imaging and monitoring relies primarily on ground surface and satellite remote sensing observations. The overall understanding of the volcanic edifice and its dynamics is thus limited by surface investigation, spatial resolution and penetration depth of the ground methods, but also by human and material resources, and harsh environments. Here, we show for the first time that an airborne electromagnetic survey provides a 3D global resistivity model of an active volcano. The high-resolution survey acquired at the Piton de la Fournaise volcano on La Réunion Island, Indian Ocean, shows unprecedented details of the internal structure of the edifice, highlighting the upwelling hydrothermal system below the craters, magma intrusion pathways and inherited faults. Together with surface monitoring, such airborne imagery have a high potential to better characterize volcano internal structure and magmatic processes, and therefore to better anticipate catastrophic events such as phreato-magmatic eruptions or volcano destabilizations.