This chapter discusses the regulation of germline editing in Europe, the only region in the world to date to have set up a regulatory framework for biomedical research. First, we consider the principal contributions of the Council of Europe to this framework. After a brief introduction of the history, goals and structure of this organization, we analyse key provisions of the Convention for the Protection of Human Rights and Dignity of the Human Being with regard to the Application of Biology and Medicine (Oviedo Convention) as well as its additional protocols. Relevant case law of the European Court of Human Rights related to the protection of human embryos is also taken into account. Then we turn to the European Union (EU) to examine its efforts to articulate a regulatory for biomedical research. Again, after a brief introduction to the EU, we discuss the basic elements of its framework. This includes the relevant rights included in the EU Charter of Fundamental Rights, the EU directive on the legal protection of biotechnological inventions (98/44/EC) and the EU regulation on clinical trials on medicinal products for human use (EU 536/2014), as well as significant case law of the European Court of Justice. Throughout our analysis, we highlight contradictions, gaps and unresolved issues of the current European regulatory framework, which slow down or even block scientific advancement on human germline modification in Europe. We conclude the chapter not only by pointing to the need for a public debate to address the challenges faced, but also by acknowledging the difficulties of making progress in the light of the complexity of the EU framework and the current political climate.