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This article focuses on the economics of digital markets with particular emphasis on those features that are commonly deemed critical for Antitrust. Digital markets are often concentrated due to network effects and due to the need of large amounts of Data for production. We review papers characterizing the nature of social harms caused by market power and the role of competition FOR the market and IN the market to relief some of that harm. Special emphasis is given to the role of (i) human attention (which is monetized and is a key input in advertising markets), (ii) Data (which is the oil that powers these markets) and (iii) innovation (incentives, entry for buyout and killer acquisitions).