The article describes the importance of modern school to develop students' problem-solving skills, including through digital tools, which in turn include the development of basic coding skills and digital literacy, the ability to solve problems and make decisions based on planning and analysis of situations. All these skills are the basis of computational thinking (CT). The authors analyze the concept of CT, existing denitions and its components. The list of subjects of curricula of different countries of the world on which the study of CT in primary school is carried out is given. It is emphasized that CT is a fundamental skill of everyone and it should be formed on the basis of integration of different disciplines to solve problems. The connection of the components of CT with the key competencies that should be formed in students by the standard of primary education. The results of a survey of more than 60 primary school teachers from different regions of Ukraine are presented about their understanding of the concept of computational thinking and their experience in the formation of skills related to all components of computational thinking in the teaching of primary school students. An analysis of open educational resources from around the world to support teachers in developing students' CT skills is presented. A model for the implementation of the concept of development of CT for future teachers and primary school teachers is presented.