The topic of this paper is the abuse of a dominant position in digital markets with special reference to self-preferencing. This topic is of great importance today more than ever because digital platforms have never in history had as much importance and influence on the market as they do today. This paper first explains the concept of a domnant position and its abuse through the practice of EUCJ and the EU Commission. The central theme and merit of the work deal with consequences of dominant digital platforms on the market and how they violate competition rules. In order to understand better anticompetitive effects, the paper presents practices that such companies use to abuse their dominant position. The paper discusses the definition of relevant market in which platforms operate and abuse their dominant position. The paper also reflects on the new legal framework regulating ex ante this dynamic sector. Self-preference, particularly harmful and frequent form of abuse of a dominant position through the decisions of the EU Commission clarifying the consequences that this practice has on the market and on all market participants. The conclusion is drawn that the combined ex ante and ex post legal regulation of this sector is welcome, despite the indentified challenges, and the legal framework will have to be updated from year to year in order to be able to follow the rapidly growing sector of digital markets.