This article is intended to delineate the place occupied by studies on the globalization of the history of anthropological ideas, based on the premise that cultural interconnections have never been absent from the concerns of anthropology, even when dealt with under the most widely diverse conceptual models. This objective is the basis for an investigation of the genealogy of the vocabulary used by transnational anthropology, unveiling the meanings and uses of three key words - flows, frontiers, and hybrids - both within anthropology and in a broader interdisciplinary context. By establishing multiple dialogues - with diffusionists, theorists of acculturation, and contemporary multiculturalist currents, amongst others, the text points to the reflexive dimension that the problematic (yet enriching) relationship between academic and native concepts has impressed on anthropology, especially through studies on globalization.