Various authors have suggested behavioural similarities between tool use in early hominins and chimpanzee nut cracking, where nut cracking might be interpreted as a precursor of more complex stone flaking. In this paper, we bring together and review two separate strands of research on chimpanzee and human tool use and cognitive abilities. Firstly, and in the greatest detail, we review our recent experimental work on behavioural organization and skill acquisition in nut-cracking and stone-knapping tasks, highlighting similarities and differences between the two tasks that may be informative for the interpretation of stone tools in the early archaeological record. Secondly, and more briefly, we outline a model of the comparative neuropsychology of primate tool use and discuss recent descriptive anatomical and statistical analyses of anthropoid primate brain evolution, focusing on cortico-cerebellar systems. By juxtaposing these two strands of research, we are able to identify unsolved problems that can usefully be addressed by future research in each of these two research areas.