This lecture was given during the inaugural session of the International Congress of Hematology, held at Santiago, 1998. It consists in a general view of the evolution Greek thought on medical practice and theory underwent from mythological times down to the Hellenistic period and the Bizantine one, also. References are made to the main streams on medical thinking that prevailed, that is schools Kos and Knido, the one synthetic, the other analytical. Special emphasis deserves here Hippocrates, his personality, methodology, and the virtues that, in his opinion, ought to inspire the medical practice.