Variation in methods and measures, resulting in past dispute over the existence of population handedness in nonhuman great apes, has impeded progress into the origins of human right-handedness and how it relates to the human hallmark of language. Pooling evidence from behavioral studies, neuroimaging and neuroanatomy, we evaluate data on manual and cerebral laterality in humans and other apes engaged in a range of manipulative tasks and in gestural communication. A simplistic human/animal partition is no longer tenable, and we review four (nonexclusive) possible drivers for the origin of population-level right-handedness: skilled manipulative activity, as in tool use; communicative gestures; organizational complexity of action, in particular hierarchical structure; and the role of intentionality in goal-directed action. Fully testing these hypotheses will require developmental and evolutionary evidence as well as modern neuroimaging data.