Long-standing speculations and more recent hypotheses propose a variety of possible evolutionary connections between language, gesture and tool use. These arguments have received important new support from neuroscientific research on praxis, observational action understanding and vocal language demonstrating substantial functional/anatomical overlap between these behaviours. However, valid reasons for scepticism remain as well as substantial differences in detail between alternative evolutionary hypotheses. Here, we review the current status of alternative 'gestural' and 'technological' hypotheses of language origins, drawing on current evidence of the neural bases of speech and tool use generally, and on recent studies of the neural correlates of Palaeolithic technology specifically.