The world has entered a period of deep transition with rapid and phenomenal development of innovations. The rise of the digital economy has dramatically changed the global business environment, creating new challenges for the tax system. Newspapers and magazines are being replaced by the Internet, and trade in material goods – by digital services. The digital economy eliminates the barriers of time, space and distance. The server where the transaction is processed, the location from which the goods or services are supplied and the place of supply of such goods or services are in different jurisdictions, therefore, the question “Where should the transaction be taxed?” is raised. Meanwhile, the digital economy opens up unprecedented opportunities to avoid taxes with the international tax rules which are still “stuck” in 20th-century business concepts, because the companies operating in the digital space do not need factories, stores or other permanent residences to develop their activities. This article aims to evaluate the efforts of the European Union and international standard-setting entities to find a solution for fair taxation of the digital economy. The first part of the article delves into the concept of the digital economy and its essential features with a special emphasis on the role of the digital service user which is unique and more complex than the role usually played by the customer. This part also analyses the differences between digital and traditional business. The second part of the study emphasizes the reasons that will lead to the necessity of taxation of the digital economy, discusses the digital services tax applied in certain countries of the European Union and highlights the weakness of the concept of digital establishment in double taxation agreements concluded by the countries. The final part explores the proposals submitted by the European Commission regarding the introduction of a common consolidated corporate tax base and the inclusion of the concept of virtual permanent establishment in the tax system in the context of the digital economy taxation model proposed by international organizations.