The tectono-stratigraphic evolution of rift systems is at present poorly understood, especially the one preceding the onset of oceanic seafloor spreading. Improving our understanding of the complex, polyphase tectonic evolution of the fossil Alpine Tethys, one of the best calibrated magma-poor rift systems worldwide, offers great potential for the interpretation of the distal part of global rifted margins, which notoriously lack data. In this paper, we propose a tectonostratigraphic model for the former Alpine Tethys, whose remnants are exposed in the Alps of Western Europe. We fist review the historical evolution of some concepts grounding present knowledge on the Alpine-and global magma-poor rifted margins. Then we present a spatial and temporal template for the Alpine Tethys rift system using a "building block (BB)" approach. This new approach is powerful in that it can integrate high-resolution, structural, stratigraphic, thermochronological and petrological observations from dismembered outcrops into a margin-scale template compatible with the first-order seismic architecture defined at present-day, magma-poor rifted margins. The detailed analysis of the syn-rift sequence of the Alpine Tethys margins demonstrates that extension migrated and localized while evolving from the stretching to the necking phase. During hyperextension, rifting was asymmetric and controlled by in-sequence detachment faulting. Then, the rift system evolved back into a more symmetric, embryonic spreading system. With this contribution, we aim to allow readers without knowledge of the Alps to access to this unique "archive" preserving some of the world's best-exposed rift structures. Recognising these structures is critical to understand the origin of some new concepts used to explain present-day, deep-water rifted margins, and to interpret and predict the tectono-stratigraphic evolution during advanced stages of rifting. Highlights: Our "building block" approach enables us to upscale local outcrop observations into a global margin template The syn-rift sequence of the Alpine Tethys margins is among the best calibrated worldwide The observed rift migration-localization has far-reaching consequences for the interpretation of global rifted margins