It is a widespread phenomenon that online platforms which enable users to upload copyright-protected content use software-based tools that automatically identify and restrict copyright-infringing user uploads based on algorithms – so-called upload filters. The European Union is currently at the forefront of the development to govern upload filters through legislation, both with regard to requiring platforms to filter infringing content (Art 17 of the Directive on Copyright in the Digital Single Market) and with regard to mitigating risks of automated filtering (especially through the newly adopted Digital Services Act). Against this background, this article analyses the European approach to algorithmic enforcement of copyright and compares it with the situation in the United States. After laying out the legal foundations from which the necessity to engage in algorithmic enforcement results, this article focuses particularly on legal approaches to avoiding the restriction of permissible content (“overblocking”).