Within the European Union, there have been significant strides in adapting competition law doctrines to address the perceived market failures and public policy concerns that might arise from certain online platforms, including ‘big data’ operations. However, there are large gaps in our understanding of how to assess problematic commercial practices on online platforms in a more holistic way. There is a risk that competition authorities might stifle innovation through excessive intervention, or allow market growth to be stunted by failing to act in the face of tangible anti-competitive practices. This article explores the growth of merger and behavioural precedents under competition rules, and the lessons from various stakeholder consultations at a national and international level. While the fundamental tools available under EU competition rules can address many concerns arising from the abuse of market power, there remain a number of analytical and institutional challenges to be addressed by antitrust policymakers in Europe.