Ostensive communication involves the expression and recognition of intentions. As such, it requires social cognitive skills of a certain degree of sophistication. Ostensive communication can be contrasted with 'code model communication', in which production and comprehensive are governed by associations, of varying degrees of sophistication. Do any other species, and in particular any of our great ape relatives, communicate in an ostensive way? In this talk, based upon arguments first developed in Speaking Our Minds (2014, Palgrave Macmillan), I will argue that ostensive communication is likely uniquely human. This in turn explains why only humans have languages: conventions that enhance the expressive potential of ostensive communication. To make these arguments I will systematically survey experimental findings on the communication of children and non-human primates, and in the process highlight some specific gaps in the experimental literature.