The paper examines the STEM approach as one of the revolutionary tools for transforming education. This paper discloses the content of the concept of “STEAM-education”, substantiates its importance and prerequisites for its appearance. The author elucidates a comparative analytical review of trends and prospects for the development of STEAM education in the Russian Federation. In this paper, the authors want to touch upon a comprehensive theoretical and methodological study conducted on the declared problem to identify the problem of the formation and development of the STEAM approach in the education system in the Russian Federation at all levels: general education, vocational education, and additional education. The object of this study was STEM education. The subject of this research was the STEM approach and STEM technologies in the system of general education, vocational education, and additional education. The methodological foundation of the study was the general scientific propositions on the holistic, systemic, and dialectical approaches to research, which made it possible to assess the totality of interrelated and interacting elements that form a certain integrity. The use of these approaches provided a comprehensive analysis and formulation of the research problem and determined the strategy for its study. The analysis of the current state of STEM and STEAM education in higher education in the Russian Federation suggests that it is necessary to stimulate the development of information and communication technologies in the country’s education system in general, as well as to develop comprehensive programs for adapting STEM and STEAM approaches among the subjects of educational relations. In the context of modern global risks and challenges, the educational trajectory of development in Russia should be conceptually consistent with the new strategy in the field of natural science education adopted in the United States, “The Path to Success: American Strategy for STEM Education”. Experts believe that through the practical implementation of STEM and STEAM technologies, it is possible to improve the efficiency of the quality of training for the purposes of the modern digital economic sphere. In this regard, the primary competences obtained in the higher education system in the areas of STEM and STEAM training should be cognitive, personal, and interpersonal competences, expressed in digital literacy, computational thinking, creativity, open mind, soft skills, and others. The concept of STEAM education in the system of higher professional education in Russia will ensure the transformation of ideas about scientific knowledge and build an innovative development process through the formation of skills in the field of exact sciences, linguistics, engineering, art, etc.