We review four studies investigating hand preferences for grasping versus pointing to objects at several spatial positions in human infants and three species of nonhuman primates using the same experimental setup. We expected that human infants and nonhuman primates present a comparable difference in their pattern of laterality according to tasks. We tested 6 capuchins, 6 macaques, 12 baboons, and 10 human infants. Those studies are the first of their kind to examine both human infants and nonhuman primate species with the same communicative task. Our results show remarkable convergence in the distribution of hand biases of human infants, baboons and macaques on the two kinds of tasks and an interesting divergence between capuchins' and other species' hand preferences in the pointing task. They support the hypothesis that left-lateralized language may be derived from a gestural communication system that was present in the common ancestor of macaques, baboons and humans.