An important proportion of Latin America's forests are in indigenous territories. Many of these are subject to threats from colonists, illegal loggers, extractive companies and others, whose practices endanger not only the forests but also indigenous people's territory as a whole - hence the importance, a priori, of indigenous territories for REDD+ and REDD+ for indigenous peoples. Indigenous territories constitute a new spatial reality that is quantitatively and qualitatively different from the community emphasis of the past. To what extent will REDD+ interventions take into account this new territorial configuration? What challenges does REDD+ face? How can REDD+ address both this new spatial scale and the great heterogeneity amongst indigenous territories?