This article surveys the state of the literature on Hume’s epistemology, focusing on treatments of what has come to be known as the ‘Kemp Smith problem’, that is, the problem of reconciling Hume’s scepticism with his naturalism. It first surveys the literature on this issue with regard to the Treatise, moving on to briefly compare the Treatise and the Enquiry in virtue of their epistemological frameworks, before finally examining the literature with regard to the first Enquiry.