The research review of the subject field on the research of the digital transformation of economic and social systems is carried out. The research includes two parts. In the frost part the conceptual and mathematical models based on them research considered to apply digital technologies for various types of activities. Based on the systematic use of the review of the subject field, a complex of “white spots” is revealed — inconsistencies of the conceptual and mathematical models necessary in practice, methods of mathematical research of digital transformation of systems of different types, on the one hand, and the available theoretical means for such research, on the other. A significant amount of such inconsistencies is caused by insufficient investigation of the complex of pragmatic, practical aspects of activity based on mathematical forecasting of the results of using modern (digital) technologies in systems of various types. We proved that a pragmatic mathematical study of activity could make it possible to design and improve the digital transformation of systems of different types. We could do such a study by evaluating the activity results, analyzing them using mathematical models, and then synthesizing the activity with mathematical methods based on the analysis of the effects of using information technologies. Such a synthesis can, for example, provide the best results of activities due to the choice of the composition and characteristics of digital technologies.

The results of the review of the subject field on the research of the digital transformation of economic and social systems is carried out (part II). We reviewed main theoretical, mathematical tools which could allow solving unsolved problems. The review of such main theoretical tools that can become the basis for developing the “activity paradigm” of research is carried out.