Recently, concerns have been raised about the phenomenon of 'overdiagnosis', the diagnosis of a condition that is not causing harm, and will not come to cause harm. Along with practical, ethical, and scientific questions, overdiagnosis raises questions about our concept of disease. In this paper, we analyse overdiagnosis as an epistemic problem and show how it challenges many existing accounts of disease. In particular, it raises questions about conceptual links drawn between disease and dysfunction, harm, and risk. We argue that 'disease' should be considered a vague concept with a non-classical structure. On this view, overdiagnosed cases are 'borderline' cases of disease, falling in the zone between cases that are clearly disease, and cases that are clearly not disease. We then develop a précising definition of disease designed to provide practical help in preventing and limiting overdiagnosis. We argue that for this purpose, we can define disease as dysfunction that has a significant risk of causing severe harm to the patient.