In this review and position paper we explore the neural substrates for manual specialization and their possible connection with language and speech. We focus on two contrasting hypotheses of the origins of language and manual specialization: the language-first scenario and the tool-use-first scenario. Each one makes specific predictions about hand-use in non-human primates, as well as about the necessity of an association between speech adaptations and population-level right-handedness in the archaeological and fossil records. The concept of handedness is reformulated for archaeologists in terms of manual role specialization, using Guiard's model of asymmetric bimanual coordination. This focuses our attention on skilled bimanual tasks in which both upper limbs play complementary roles. We review work eliciting non-human primate hand preferences in co-ordinated bimanual tasks, and relevant archaeological data for estimating the presence or absence of a population-level bias to the right hand as the manipulator in extinct hominin species and in the early prehistory of our own species.