Digital technologies and their tools are fundamentally changing not only the technological order, but also the economic system. Recently, researchers and the business community attention has been focused on digital companies born in the era of the modern Internet and offering value propositions based on digital technologies and their cross-border properties. But how multifaceted and heterogeneous the nature of the technologies is, so complex and multidimensional is the process of their implementation, which transforms not only the company’s IT environment, but also the whole strategic management system. In the process of this transformation, companies face a range of challenges that can lead to devastating consequences. Understanding the sources and nature of these challenges allows to find ways to overcome them and transform them into competitive advantages. The structure of the article includes two blocks. The first block summarizes evolutionary ideas about transformation through its main constructs, parameters, and stages. The second block shows the study and systematization of the challenges that lead the waves of digital transformation in the context of their impact on the parameters of the strategic management system.