Given the boundless amount of scientific information, clinical skills, and interventional techniques present in biomedicine today, it is impossible for individual physicians and clinicians to have absolute medical knowledge. Further, ambiguity in the interpretation and treatment of illness can lead to significant uncertainty. Despite the inevitability of not knowing in biomedicine, however, there is relatively little academic discussion about how physicians are socialized to address ignorance, how clinicians experience gaps in knowledge as practitioners, or the various forms that not knowing takes in professional health-care practice and education. This article seeks to invigorate new discussions on the role of ignorance and "non-knowledge" in biomedical practice and training. The article critically examines the predominant focus on medical knowledge in the sociological literature and presents a new anthropological framework for the relationship between knowing and not knowing in medicine, called "sufficient knowledge." The author posits that future social and humanistic examinations of biomedicine should seriously consider the ways that physicians navigate ignorance, uncertainty, and not knowing, and that scientists, clinicians, social scientists, and ethicists all have valuable disciplinary perspectives to bring to the conversation around medical ignorance.