To date, a lack of reliable morphological and geophysical data has been a major limitation to understanding the tectonic and magmatic processes that shape the Azores Triple Junction and the Terceira Rift. This situation has changed recently: for the first time both areas are covered by high-quality swath bathymetry surveys and marine magnetic data with GPS quality positioning. This provides a good description of the surface morphology, and also of magnetic chrons that give fundamental information for the timing of spreading processes in a geological time frame. There is also a large amount of data from GPS stations that provide accurate estimations of present-day velocities for most of the islands. It is shown that only two main rift systems can be found on the plateau, the older one matching the Princess Alice Basin, and the newer one matching Terceira Rift; the shift between the two probably occurs close to c. 3 Ma. It is shown that extension is currently concentrated on the Terceira Rift, progressively attaching Graciosa and Terceira islands to Eurasia, while São Miguel is being strained by rifting. It is also shown that no right lateral strike-slip fault connects the Terceira Rift to the Mid-Atlantic Ridge.