The article deals with the issue of abuse of dominant position by undertakings in the European Union market. The Treaty on the functioning of the European Union prohibit any abuse by one or more undertakings of a dominant position within the internal market or in a substantial part of it because it may affect trade between Member States. But it doesn’t state about the definition of dominant position and abuse of it. It also doesn’t make clear the situations when abuse of dominant position takes place. The article clarifies the meaning of dominant position and defines the way in which it can be established. The author makes an attention on the main and additional factors due to which an undertaking may be considered as in dominant position. There is also stated that taking by an undertaking a dominant position is not anti-competitive conduct. But if it uses this position to eliminate competitors from a market or to make other actions that contradict to the fair competition, it is considered to abuse it. Thus, the article determines what is the abuse of dominant position and in which form it can appear. It also indicates the situations in which enterprise can occupy a dominant position in one market, but abuse of its dominant position may happen through actions in another market. Such situations usually appear during exploitative abuses. The Treaty on the functioning of the European Union provides some mods of abusive conduct. But the provided list is not exhaustive. Due to this the article also distinguishes the types of abuse of the dominant position – horizontal and vertical. It also reflects the categories of abuses such as exclusive dealing, tying, bundling, predatory conditions, refusal to supply. The author reveals the questions in the issue in the light of the practice of the European Commission and the Court of Justice of the European Union.