The present article offers a condensed overview, of why a comparative view on gestures in human and nonhuman primates may offer important insights to both: researchers of human as well as of nonhuman primates. It is argued that a comparative view may further contribute to the debate over the evolution of language but that in addition it may also enhance understanding of the relation of language and gesture in humans. The article sketches programmatic issues, which are summarized in the list of framing questions for the workshop and this special issue on “Gestural communication in nonhuman and human primates”; it is aimed to clarify conceptual and methodological prerequisites and to offer points of departure for future comparative research.