This paper aims to highlight the main challenges posed by the Big Tech companies, since the traditional businesses and the civil society are increasingly dependent on large online platforms without remotely comparable bargaining power. The ever-expanding role and the extraordinary market power of Big Tech has generated legitimate legal, political, social and business concerns as they play a vital role for international economic decisions. With my work I analyze one of the biggest concerns for Antitrust law: the risk of abuse of dominant position by these Digital Giants who are endowed with enormous power. In addressing this issue, I compare the European approach with the US’s one, and at the same time, I highlight how, in my opinion, the private enforcement channel -if revisited in a modern way-can become an effective tool to protect the interests of consumers (who represent the weak contractors). Furthermore, I underline another aspect that antitrust law should consider: the possibility that digital giants abuse their power, exploiting it to obtain more and more consumer data, which today are the greatest source of wealth. In conclusion, recalling the debate on the objectives of Antitrust law, I highlight how, thanks to its flexibility, competition policy can reconcile: the need to promote innovation, variety of offers, freedom and autonomy of strategic choices, with the protection of consumer interests. Precisely, competition law, must be able to safeguard the innumerable advantages resulting from the advent of the digital era, and at the same time, prevent the prejudice that certain Digital Giants’ behaviors have on "consumer welfare" (as well as on "social welfare").