The European Commission has proposed a new regulatory tool for the governance of digital markets. The Digital Markets Act (DMA) intents to limit the market behavior of so-called gatekeeper companies to ensure contestable and fair digital markets. We review the provisions of the DMA both from a legal and from an economics perspective. Notwithstanding a number of benefits, we identify several issues with the current proposal. When looking at the core provisions of the proposal from an economic perspective, five issues of contention arise: many of the provisions seem to be quite narrow in scope and it seems difficult to extrapolate more general rules from them; the economic harm of some of the provisions is both uncertain and in principle debatable; the alleged distinction between different types of obligations cannot be verified, and, last but not least, while the DMA seeks to control existing gatekeepers, the “tipping” of markets and the rise of further gatekeepers is not guaranteed by this proposal; this in turn leads to a larger critical analysis of the gatekeeper as DMA’s norm addressee. From a legal perspective, the first hurdle is the lack of clarity pertaining to the nature and goals of the DMA, this is further compounded by procedural provisions and an enforcement regime with many uncertainties and loopholes – all of which tend to undermine the intended stringency of the regulation and its overall chances of making digital markets systemically more contestable and fairer. Thus, we think that a reform of the competition policy regime would better suit the need of regulating big tech.