The relevance of the topic is due to the comprehensive development of digital technologies and the need for timely legal regulation of new phenomena of public life. Digitalization is not only rapidly penetrating all sectors of the economy, but is a trigger for the creation of qualitatively new economic relations. The digital transformation of the economy and markets, in addition to objective advantages, also carries negative consequences. Negative manifestations are possible in the monopolization of commodity markets. Antitrust laws are changing in line with the expansion of digital markets. The article identifies the main obstacles to regulating monopolies in the digital economy. The practice of antimonopoly regulation of digital platforms is considered. The tasks of adopting the fifth antimonopoly package as expanding the scope of the Federal Law On Protection of Competition are outlined. In addition, the concept of economic concentration is analyzed, as well as signs of restricting competition when considering transactions in its conditions. Particular attention is paid to differences in approaches to regulating the digital market in Russia, France and USA. A comparative analysis of the antimonopoly legislation of Russia, France and USA, types of economic concentration, regulations for control over concentrations at the level of different jurisdictions has been carried out. The phases of control over economic concentration, the powers of the antimonopoly authorities, the assessment of criminal encroachments on competition are considered in detail.