Digital markets development all over the world reveals trends of Big Tech companies' enhancement therein, both transnational and domestic. Applying innovations Big Tech companies can accumulate their users' data enormously and then process them, which finally constitutes a highly demanded product known as Big Data. There is no uniformed approach to Big Tech companies' activity. Doubts arise about preserving fair competition in digital markets, while online platforms and over Big Tech companies hold power concentration. It should be noted that the legal criteria of links between the market influence of Big Tech companies, especially online platforms, and their anti-competitive actions must be determined. This paper substantiates the Big Tech companies' leadership in digital markets is to be considered through antitrust law. Thus, "Big Data dominance" doctrine reasoning why it is essential to regulate within antitrust law Big Tech companies' activities as online platforms in the data market should be developed. Special attention is devoted to the specifics of Big Tech companies being online platforms operating. Their activity in the data market gives rise to some network effects that should be considered while developing new criteria for dominance in digital markets. At the same time, network effects act as access barriers to large online platforms, and, consequently, to the Big Data that they accumulate. The Big Data is crucial for the incorporation and expansion of data-based businesses, as well as for improving public services rendering. Therefore, ensuring non-discriminatory access to the big data becomes a vital task, the development of the digital markets depends on. At the same time, the use of Big Data should not infringe on the rights of the citizens to protect data achieved through anonymisation. While enormous aggregation of data grows in its significance for businesses and private individuals, different states are seeking to provide appropriate legal regulation for Big Data application by digital platforms. The article calls for antitrust laws uniquely tailored to the tech industry in order to democratize access to data and provide room for future disruptors to enter the market. The question arises whether a balance for legal restrictions for access to anonymised data, personal data, and freedom of enterprise and business. Herein, the promotion and marketing of goods and services are noteworthy.

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The article deals with the problems of legislation establishment that ensure the formation and development of Russia's digital economy. Also, the concept of the "digital economy" is investigated, and a scientifically-based approach to its definition is formed. It is proposed to consider only those economic relations, which object is the new economic benefits created and functioning with the use of digital technologies as the core and the essence of the digital economy. The authors distinguish digitalization processes, which means the introduction of digital technologies, and the methods of automation and electronic document management. The article explores international leading experience in the legal regulation of new economic phenomena from the application of digital technologies. At the same time, the possible risks are also revealed, particularly technical errors and vulnerabilities in blockchain platforms that hackers can exploit. The process of economy digitalization has led to the formation of new property circulation objects, which have acquired a common name of digital assets. The article analyzes the "digital rights" category, which intermediates new objects of property circulation having digital nature. It reveals the legal digital rights definition's main drawbacks, which cause legal uncertainty for crypto investors. The authors conclude that the new Russian legislation on digital rights does not contribute to the harmonization of law in the digital economy, deprives Russia of the leading position in this sphere, and may negatively affect the investment prospects of the Russian digital assets market.