Abstract This paper aims at calling geographers' attention to the works of Italian historical demographer Massimo Livi Bacci, who authored fundamental texts on the indigenous genocide in the Americas, on the history of world population, on global migrations and on population's environmental ‘sustainability’. In denouncing colonial crimes, critically questioning commonplaces of Malthusian origin and challenging sovereignist prejudices against migrations, Livi Bacci stresses the need for scholars to fully address the complex relations between space and population in both analyses of empirical cases and elaborations of broader theoretical models. He explicitly raises geopolitical matters on the potential political consequences of demographic and migratory dynamics. Yet, Livi Bacci's huge scholarly production is highly influential among historians and demographers, but seems to have been overlooked by most geographers hitherto. For these reasons, I argue that scholars committed to critical, radical and decolonial geographies of population (past and present) should (re)discover Livi Bacci's contributions. Re‐reading Livi Bacci's works through geographical lenses and connecting them with current geographical scholarship, I show how ‘geo‐demography’ can help geographers to address demographic matters at different scales, by providing insights for a new critical geo‐history of population. This interdisciplinary engagement with the relations between geopolitical matters on sustainability and the ongoing changing in global population has the potential to plurally nourish critical geographical agendas, including on global migrations and colonial legacies.