In the last decade, the concept of digital economy has become widespread in research and practice of a number of the countries. Rapid development of digital technologies against the backdrop of economic globalization laid the foundations for digital revolution and for information becoming the primary, rather than the auxiliary, resource for market participants. Transition to digital economy entails digitalizing the business processes, introducing digital technologies in industrial enterprises, service companies, government bodies and financial institutions. Developing digital technologies provides indisputable advantages for economic subjects, increasing the efficiency of economic processes, increasing competitiveness, producing the synergetic effect due to network interaction between market participants, expanding the opportunities for using digital payment systems and digital money. Despite active development of digital technologies in all areas of economic activity, their opportunities, advantages and shortcomings have not been sufficiently studied. Theorists and practitioners continue discussions about the prospects of digitalization and possible risks connected with transition to digital technologies in strategically significant spheres of economy, in particular, in banking and financial sectors where the blockchain technology finds application. Data and other factors confirm the importance of the study subject. We have established that, as digital economy is evolving in Russia, blockchain as a special technology opens up new opportunities for various economic subjects, including the participants of the financial market, and also provides advantages in saving time and resources when performing financial operations. We have discussed the stages of evolution of bitcoin which is based on the blockchain technology and also the stages of introduction of cryptocurrencies in Russia.