The study of ancient Greek medicine, with undiminished importance for the History of Science and renewed one for the alternative approaches it may suggest, suffers from a set of unwarranted beliefs which, little by little have become established. The main points are the strong belief of the religious dimension of the early practices, under the name of Asklepios and the subjective relation with the respective practices of Egypt and Mesopotamia, or the certainty of a clear break or discontinuity of the Hippocratic medicine of classical Greece, with the Asklepiad’s religious past and practices. Furthermore, there is a notion of rejecting most of the ancient Greek procedures as products of empiricism and charlatanism, with plant juices and incantations instead of modern type drugs. And finally it was suggested that the low number and level of the achievements after two or three centuries of secular medical practice, is rather mediocre before the Roman medicine jump-started it. These topics are the focal points covered in the chapters of this book.