Abstract The significance of symmetry to understanding the cognitive profile of the hominins responsible for making Acheulean handaxes has been contentious. Recent finds and analytical techniques have allowed a reassessment of the relevance of symmetry to evaluating the cognition of archaic humans by highlighting differences in the shape of Early to Late Acheulean bifaces. In this paper, I critically examine issues regarding the symmetry of handaxes as well as models of cognitive evolution that refer to the structure of Acheulean bifaces.