The complexity and emergent autonomy of Generative AI systems introduce challenges in predictability and legal compliance. This paper analyses some of the legal and regulatory implications of such challenges in the European Union context, focusing on four areas: liability, privacy, intellectual property, and cybersecurity. It examines the adequacy of the existing and proposed EU legislation, including the Artificial Intelligence Act (AIA), in addressing the challenges posed by Generative AI in general and LLMs in particular. The paper identifies potential gaps and (...) shortcomings in the EU legislative framework and proposes recommendations to ensure the safe and compliant deployment of generative models. (shrink)