The article examines some pivotal aspects of Directive (EU) 2019/790, which is the new legislative act adopted by the European Union to adapt copyright to the evolving digital environment. Indeed, this measure is meant to have considerable implications on the European plane and is supposed to influence, at least in part, also the relations between the EU and third States in the field of copyright. The Directive shall be transposed by mid 2021, but the time is ripe for a first assessment and some reflections. The analysis primarily investigates the relationship between Digital Single Market and EU copyright law and focuses on the most controversial issues of a long-awaited piece of legislation that so far has been widely criticized. In particular, the article explores three new key points: mandatory exceptions and limitations to right holders’ exclusive rights, press publishers’ rights, and platforms’ liability.