We now know more than ever about how Neanderthals disappeared and how our species successfully expanded across a single, enormous piece of land called Eurasia. Nevertheless, challenges remain in assessing how it all unfolded across this combined landmass. To address these obstacles, the EU-funded FINISTERRA project will focus its studies on the Iberian Peninsula, which is considered one of the last refuge zones of Neanderthals. It will introduce high-resolution data on the events that caused Neanderthals’ final disappearance, explore the existence of early warning signals of their demise and investigate other hypotheses about how they steadily or abruptly lost their resiliency.