This article examines the impact of digital platforms (marketplaces) created in the conditions of network economy in its new “center–periphery” configuration upon the consumer markets and provisions of competition law applicable to digital markets, using the experience of foreign countries (Germany, Asia, Latin America, etc.) and integration associations (the European Union), including from the perspective of new law enforcement (judicial) practice, based on the fact that its knowledge allows successful resolution of the essential problems of legal regulation in the Russian Federation. Attention is given to such aspects of the activity of digital platforms (Amazon, Apple, Facebook, Google etc.), as the dependence of their market influence on the network effects associated with utilization of the user data, supported by market practices, such as vertical integration and amalgamation of companies that are capable of reducing market competition. Assessment is given to the degree of readiness of the countries and their associations to operate in the conditions of digital platforms. The relevance, theoretical and practical importance of this research are substantiated by the emergence of new competitive practices (digital platforms) that can influence the competition. The author concludes that due to the “network effect”, digital platforms have an inexhaustible range of capabilities for acquisition of the dominant position on the market and its abuse. These include the formation of consumer groups of targeted advertising and sales of their services; as well as setting personalized prices based on determination of the readiness and limit of individual payment; and usage of data on the products of vendors on their platform to score an advantage in selling their products, etc.