Large-scale digitization of the economy produces a strong influence on competition. On the one hand, the spread of benefits that could not emerge without Digital, intensifies contentiousness. Country borders are erased, the choice of products and services is increasingly getting broader, and their search and comparison is becoming faster and easier. It took the Mariott chain almost 70 years to secure strong positions in 26 countries, and Airbnb activated its presence in 89 countries within 3 years. And distruptive business models instantly change the whole value chain of industries, just as Airbnb did. On the other hand, there is the risk of market concentration and non-transparency: digital platforms can quickly scale the business, and data collection allows to manipulate customer choices and keep them on the hook. The speed and the difficulty of regulating digital markets set new tasks to antitrust services. What are the key challenges and how can we respond to them?