This study raises the question of the contemporary perception of the ideas of the philosophy of science (within the framework of the three waves of positivism and the early postpositivism) by researchers and methodologists. Firstly, I am trying to highlight the positions to the scientific process of positivists (as well as discussions around them): prescribing rules to science (O. Comte, logical positivists, K. Popper), studying foundations of science to overcome its crisis (P. Duhem and empirio-criticists), as well as the researching the scientific process by building models and taking into account various factors influence science (T. Kuhn, I. Lakatos, P. Feyerabend). Secondly, I am assessing how several modern theories and conceptions (especially, the ideas of V. M. Allakhverdov, A. S. Karmin, and Yu.M. Shilkov) interact with the legacy of positivism: researching the scientific process or solving the problem of demarcation and providing principles of scientific knowledge. As a result, I state the problematic character of perception of the positivists legacy: some resea