The Azores archipelago occupies a lateral branch of the Mid-Atlantic Ridge near the triple junction of three large tectonic plates, the North American, the Eurasian and the African plates. The tectonic setting is even more complex because of the existence of the Azores hotspot and hotspot–ridge interaction. However, the hotspot origin at depth as a plume and its lateral extent are controversial subjects. High-resolution tomographic models, through the mapping of low-velocity and anisotropy anomalies, can provide an important hint to evaluate the depth and lateral extent of plumes when they exist. Therefore, we present a review of the Azores deep seismic structure as inferred from recent global and regional studies. The mapping of S-wave negative velocity anomalies in various models reveals a negative anomaly beneath the Azores confined within the upper 250–300 km. Considering the time evolution of a plume, this low-velocity anomaly might be the signature of a present-day dying plume, which created the Azores plateau 20 Ma ago. However, tomographic investigations have reached the limit of resolution provided by the global and regional seismic coverage available today. Only a long-term deployment (several years) of several broadband seismic stations in the Archipelago and on the surrounding seafloor will provide the increased resolution to better characterize plume geometry.