The review article analyses the regulation of AI training data in Europe in view of its growing economic importance. It sheds light on how the European Data Strategy and various secondary legal acts such as the GDPR, the Data Act, the DGA, the DMA and especially the AI Act try to shape access to data and its use for AI training. Definitions of data, the technical background of machine learning and associated risks such as discrimination and invasion of privacy are discussed. The article examines the area of tension between data protection and data availability and draws conclusions about the current legal situation and conceivable future developments.