Abstract Subduction initiation is a cornerstone of the Wilson cycle. It marks the turning point in an ocean's lifetime, allowing its lithosphere to be recycled into the mantle. However, formation of new subduction zones in Atlantic-type oceans is challenging, given that it commonly involves the action of an external force, such as the slab pull from a nearby subduction zone, a far-field compression, or the impact of a plume. Notwithstanding, the Atlantic already has two subduction zones, the Lesser Antilles and the Scotia arcs. These subduction zones have been forced from the nearby Pacific subduction zones. The Gibraltar arc is another place where a subduction zone is invading the Atlantic. This corresponds to a direct migration of a subduction zone that developed in the closing Mediterranean Basin. Nevertheless, few authors consider the Gibraltar subduction to be still active because it has significantly slowed down in the past millions of years. Here, we use new gravity-driven geodynamic models that reproduce the evolution of the Western Mediterranean, show how the Gibraltar arc formed, and test if it is still active. The results suggest that the arc will propagate further into the Atlantic after a period of quiescence. The models also show how a subduction zone starting in a closing ocean (Ligurian Ocean) can migrate into a new opening ocean (Atlantic) through a narrow oceanic corridor. Subduction invasion is likely a common mechanism of subduction initiation in Atlantic-type oceans and a fundamental process in the recent geological evolution of Earth.