The evolution of speech remains an elusive scientific problem. A widespread notion is that vocal learning, underlined by vocal-fold control, is a key prerequisite for speech evolution. Although present in birds and non-primate mammals, vocal learning is ostensibly absent in non-human primates. Here we argue that the main road to speech evolution has been through controlling the supralaryngeal vocal tract, for which we find evidence for evolutionary continuity within the great apes.