A frequent starting point of the ongoing debates on a future platform regulation – in the EU in the form of a “Digital Markets Act” (DMA) – is the alleged ineffectiveness of competition law enforcement in the digital realm, and in particular when it comes to “abuse of dominance” or monopolization proceedings against the largest digital platforms. This paper aims to do add to this debate in two ways : In a first part, it provides a rough overview of the competition law cases on unilateral practices in digital markets that have been initiated and partly completed over the last 10 years or so, with a strong focus on cases against large digital platforms. While there is a focus on the EU and its Member States, the overview also looks at relevant cases in other jurisdictions like the U.S., Australia, India, Russia and China in order to give an impression of the global enforcement dynamics. The overview – which is mostly based on the Concurrences database, with only some additional research on our part, which is by necessity selective – does not dive into a discussion of the merits of the cases. Rather, it is meant to systematize the enforcement actions and to provide a clearer picture when, where and why action has been taken on which grounds. A second part strives to draw some tentative conclusions from this overview against the background of ongoing policy debates. Has enforcement indeed been intolerably slow ? Does the enforcement panorama indicate what’s special about ensuring undistorted competition in the presence of gatekeepers and why we might need a special regime of platform regulation ? Does it tell us something about the optimal scope of such a regulation, and about the interaction of competition law, the law on unfair business terms and consumer protection law in the digital realm ? Does it hold insights about what we can expect from public and private enforcement respectively ?