This study addresses the relationship between the General Data Protection Regulation (GDPR) and artificial intelligence (AI). After introducing some basic concepts of AI, it reviews the state of the art in AI technologies and focuses on the application of AI to personal data. It considers challenges and opportunities for individuals and society, and the ways in which risks can be countered and opportunities enabled through law and technology. The study then provides an analysis of how AI is regulated in the GDPR and examines the extent to which AI fits into the GDPR conceptual framework. It discusses the tensions and proximities between AI and data protection principles, such as, in particular, purpose limitation and data minimisation. It examines the legal bases for AI applications to personal data and considers duties of information concerning AI systems, especially those involving profiling and automated decision-making. It reviews data subjects' rights, such as the rights to access, erasure, portability and object. The study carries out a thorough analysis of automated decision- making, considering the extent to which automated decisions are admissible, the safeguard measures to be adopted, and whether data subjects have a right to individual explanations. It then addresses the extent to which the GDPR provides for a preventive risk-based approach, focusing on data protection by design and by default. The possibility to use AI for statistical purposes, in a way that is consistent with the GDPR, is also considered. The study concludes by observing that AI can be deployed in a way that is consistent with the GDPR, but also that the GDPR does not provide sufficient guidance for controllers, and that its prescriptions need to be expanded and concretised. Some suggestions in this regard are developed.