After a brief analysis of the essence of the medical action and its different modalities (spontaneous, empirical, magic - religious and scientific or Hippocratic) a short description of the circumstances that made possible the establishment in Greece of Medicine as an art-science discipline is made. Some of the influential leaders that made possible this achievement of the human intelligence, since Asclepius to Hippocrates are mentioned. Finally the corrent trens of the evolution of scientific Medicine are discoursed.