Europe has taken a clear stand that we want AI, but we do not want just any AI. We want AI that we can trust. This talk will present the European approach to Trustworthy AI and give an overview of some of the interesting research problems related to Trustworthy AI. Special emphasis will be placed on the need to integrate reasoning and learning to combine the power of data-driven methods with the formal guarantees and general solutions provided by reasoning-based approaches. The successful realization of Trustworthy AI will be paramount for addressing the major challenges we as a global society is facing. The talk is partly based on the ongoing work in the H2020 ICT-48 network TAILOR which has the goal of developing the scientific foundations for Trustworthy AI through integrating learning, optimisation and reasoning.