The article reflects on the question to what extent the complex reality of online platforms undermines the foundations of EU competition law, which are the presuppositions of neoclassical economics and the targeting of competition protection towards greater efficiency and the resulting consumer welfare. It works first with the EU documents that relate to the regulation of large online platforms (internet gatekeepers) in the European Union and then with the teachings of complexity economics, which seems to fit the realities of the online world better than neoclassical economics. The purpose is to ask whether modern competition law could draw inspiration and recommendations for its adaptation to online realities from complexity economics. It concludes that, for the time being, this is more of a research agenda or discussion platform and only the future will show whether the lessons of complexity can be usefully applied to the formulation of legal rules and standards.