Technology giants have an ever-increasing power over our everyday lives. From search engines to social media, from e-commerce to the most widely used software application stores, online platforms offer the possibility of unprecedented consumer welfare. However, data-driven network effects, economies of scale and scope and user lock-in effects make digital markets prone to tipping, with a single dominant provider emerging. These incumbents can further entrench their gatekeeper status through killer acquisitions and by abusing their dominant market position. With the Digital Markets Act entering into force in 2023, this paper aims to provide an overview of the characteristics and unfair practices of online platforms. Although the exact consequences of this novel regulation cannot be foreseen, the paper concludes with the proposal of a holistic regulatory and enforcement approach in order to effectively tackle platform power.