The European Union institutions have many times expressed their interest in the economic growth potential of Artificial Intelligence (AI) technologies, but also in protecting the European citizens from the respective risks. The existing rules do not seem adequately equipped to address them and there is a call for action in this new regulatory field at the EU level. The study presents the most important initiatives of the European Union institutions in the field of non-contractual liability for damage caused by the application of AI technologies. Thereby, it takes part in the debate on the possible features of a new system of liability for damages caused by AI technology and attempts a first assessment of the path towards the creation of this new EU liability system.