Graph neural networks (GNNs) have rapidly taken over the field of graph mining and have found many applications in domains such as recommender systems, molecular simulation, and computer vision. This raises questions of how safe GNNs are for real-world applications. This talk discusses the reliability of GNNs, specifically their robustness with respect to adversarial attacks. We show how to obtain robustness certificates for perturbations of the node attributes as well as changes to the graph structure, and how to train up to 4x more robust GNNs.