This research concerns with the demarcation problem which was proposed by the Anglo-Saxon philosophy of science in the twentieth century. Astrology as a case study is relevant to enrich this debate and to reveal its dificulties since various philosophers of science - as Popper, Kuhn, Feyerabend, Thagard, and Laudan - have used astrology as an example to account for demarcation problem or to question it. Therefore the goal of this dissertation is to clarify a little bit more the problem of distinguishing science from non- science, in particular the case of astrology, and to examine the pertinence of this discussion in the current context of the science studies. This survey is inserted into the contemporary epistemological dialogue and it intends to contribute to a better understanding of what is science and which are your frontiers, as well to give a more precise and less prejudicing view of astrology.