How can we study significant cognitive differences within social groups anthropologically? Attempting to do so challenges some of the discipline’s most cherished methodological, analytical and ethical commitments, raising questions about how we understand difference, both between and within societies. Such challenges both explain the neglect of the topic up until now and suggest its scholarly potential. In this article, we move to lay the groundwork for an anthropology that takes seriously cognitive differences (such as autism, dementia and intellectual disability), as well as their potentially disabling consequences. We ask: what kind of cross-cultural reality does cognitive variation have, and how problematic are such differences for those who live with them? We spell out at greater length some of the difficulties involved in developing this conversation, attempt to address these issues, and delineate some of the important benefits that follow from doing so.