The advent of Generative AI, particularly through Large Language Models (LLMs) like ChatGPT and its successors, marks a paradigm shift in the AI landscape. Advanced LLMs exhibit multimodality, handling diverse data formats, thereby broadening their application scope. However, the complexity and emergent autonomy of these models introduce challenges in predictability and legal compliance. This paper delves into the legal and regulatory implications of Generative AI and LLMs in the European Union context, analyzing aspects of liability, privacy, intellectual property, and cybersecurity. It critically examines the adequacy of the existing and proposed EU legislation, including the Artificial Intelligence Act (AIA) draft, in addressing the challenges posed by Generative AI in general and LLMs in particular. The paper identifies potential gaps and shortcomings in the legislative framework and proposes recommendations to ensure the safe and compliant deployment of generative models, ensuring they align with the EU’s evolving digital landscape and legal standards.