MobiLithics is a multiscalar project aimed at characterizing the lithic resources exploitation and territorial adaptive responses among the last Homo neanderthalensis and Homo sapiens to different climatic, cultural, and biological dynamics. The project focuses on the Middle-to-Later Stone Age, in North Africa, and the Middle to Upper Palaeolithic Transition in the Mediterranean basin of the Iberian Peninsula, as key scenarios for the origin and expansion of our species. Results on geospatial modelling, petrographic and geochemical analyses, and multivariate statistics and predictive models determine the variability on resource procurement and territorial structure. These will contribute to the international debate on the adaptability of our species to different palaeoenvironments, sociocultural realities, and changing climatic conditions.