Competition Commissioner, Margrethe Vestager, has labelled digitization the “one big change that overshadows everything else.” There is healthy debate among the competition law community as to whether such statements are exaggerated. Indeed, an alternative perspective is that competition law is flexible enough to deal with issues in the digital sector without any significant amendments in approach but rather by simply applying the existing rules in a flexible and appropriate manner. Competition authorities across the globe are increasingly devoting substantial resources to try to understand the issues posed by digitisation and to ensure effective competition in digital markets. For example, to be better equipped to deal with what it sees as the novel challenges posed by digital markets, the EU Commission appointed three expert advisors to prepare a report on “Competition policy for the digital era” which was published in April 2019. As this report is the only such report at EU level (there are several other national reports), section one of this article analyses the findings of the report in some detail. In section two, we focus on one of the principle issues regulators are grappling with in the context of digital markets: that is, ensuring effective competition in situations where a platform business also competes in other markets with companies that depend on that platform. In this section, we pay particular attention to the risk of regulation being introduced to remedy the concerns identified by competition regulators and discuss the recently adopted (June 2019) EU regulation on digital platforms.