This paper examines the legal and regulatory implications of Generative AI and Large Language Models (LLMs) in the European Union, focusing on liability, privacy, intellectual property, and cybersecurity. It evaluates the adequacy of existing and proposed EU legislation, including the Artificial Intelligence Act (AIA), in addressing the challenges posed by Generative AI. The paper identifies gaps and shortcomings in the EU legislative framework and proposes recommendations to ensure the safe and compliant deployment of generative models. Generative AI, particularly LLMs, has transformed the AI landscape due to their ability to process diverse data formats and generate content across various domains. However, their complexity and emergent autonomy introduce challenges in predictability and legal compliance. The AIA aims to address these issues by regulating the design, development, and deployment of AI models, including Generative AI. However, the AIA's current text is not fully equipped to govern LLMs effectively, and further improvements are needed in the next legislative phases. The paper discusses key legal and regulatory concerns regarding liability, privacy, intellectual property, and cybersecurity. For liability, the AIA and related proposals aim to establish a framework for holding AI developers and deployers accountable for damages. However, the current framework may be too stringent for some models, suggesting the need for exemptions. The paper also highlights the need for a more nuanced approach to risk classification, considering the specific deployment contexts of Generative AI models. Regarding privacy and data protection, Generative AI models pose significant challenges due to their training on personal data and the potential for data leakage and model inversion. The paper discusses the legal basis for AI training on personal data, the need for appropriate data governance measures, and the challenges of implementing the right to erasure. It also addresses the protection of minors and the importance of purpose limitation and data minimization in ensuring GDPR compliance. In terms of intellectual property, the paper highlights the legal challenges posed by the "creative" outputs of LLMs, including the use of training datasets that may contain copyrighted material. The paper suggests that the EU legislation needs to address these issues to ensure fair use and protect the rights of content creators. Overall, the paper emphasizes the need for a comprehensive and adaptive regulatory framework that can effectively address the unique challenges posed by Generative AI and LLMs in the EU context.This paper examines the legal and regulatory implications of Generative AI and Large Language Models (LLMs) in the European Union, focusing on liability, privacy, intellectual property, and cybersecurity. It evaluates the adequacy of existing and proposed EU legislation, including the Artificial Intelligence Act (AIA), in addressing the challenges posed by Generative AI. The paper identifies gaps and shortcomings in the EU legislative framework and proposes recommendations to ensure the safe and compliant deployment of generative models. Generative AI, particularly LLMs, has transformed the AI landscape due to their ability to process diverse data formats and generate content across various domains. However, their complexity and emergent autonomy introduce challenges in predictability and legal compliance. The AIA aims to address these issues by regulating the design, development, and deployment of AI models, including Generative AI. However, the AIA's current text is not fully equipped to govern LLMs effectively, and further improvements are needed in the next legislative phases. The paper discusses key legal and regulatory concerns regarding liability, privacy, intellectual property, and cybersecurity. For liability, the AIA and related proposals aim to establish a framework for holding AI developers and deployers accountable for damages. However, the current framework may be too stringent for some models, suggesting the need for exemptions. The paper also highlights the need for a more nuanced approach to risk classification, considering the specific deployment contexts of Generative AI models. Regarding privacy and data protection, Generative AI models pose significant challenges due to their training on personal data and the potential for data leakage and model inversion. The paper discusses the legal basis for AI training on personal data, the need for appropriate data governance measures, and the challenges of implementing the right to erasure. It also addresses the protection of minors and the importance of purpose limitation and data minimization in ensuring GDPR compliance. In terms of intellectual property, the paper highlights the legal challenges posed by the "creative" outputs of LLMs, including the use of training datasets that may contain copyrighted material. The paper suggests that the EU legislation needs to address these issues to ensure fair use and protect the rights of content creators. Overall, the paper emphasizes the need for a comprehensive and adaptive regulatory framework that can effectively address the unique challenges posed by Generative AI and LLMs in the EU context.