As new generalizations of traditional deep neural networks to graph structured data, Graph Neural Networks (or GNNs) have demonstrated the power in graph representation learning and have permeated numerous areas of science and technology. However, GNNs also inherited drawbacks of traditional deep neural networks including lack of interpretability and vulnerable and unstable to adversarial attacks. These drawbacks have raised tremendous concerns to adopt GNNs in many critical applications pertaining to fairness, privacy, and safety. Though there are very recent efforts on the research of GNNs in terms of interpretability and vulnerability and building stable GNN models (or stability), these studies are still at the stage of initial development and a comprehensive investigation of these new frontiers of GNNs is critically desired. This project aims to tackle the major drawbacks of GNNs and greatly enlarge their usability in critical applications. To achieve the research goal, we systematically investigate the primary directions of GNNs including new mechanisms to interpret GNNs, and ingenious strategies to attack and secure GNNs. Each direction will dramatically extend the frontier through not only studying original problems, but also developing innovative solutions. The significance of the project lies in the fact that the project offers the first comprehensive investigation on these new frontiers and the designed novel methodologies and tasks will deepen our understanding on the inner working mechanisms of GNNs and contribute to real-world applications. The success of this project will be (1) New interpretable and stable GNNs with state-of-the-art predictive performance; (2) Theoretical analysis such as convergence and complexity; and (3) Open-source implementations of all key algorithms and frameworks. The proposed research agenda provides new perspectives for graph neural networks research, investigates original problems that entreat innovative solutions, and paves the way for new research endeavors to effectively tame graph structured data for discovering actionable patterns and harnessing them for advancing related applications. The results of this project will largely push the research boundaries of GNNs in terms of interpretability, vulnerability and stability and maximally mitigate people’s concerns on adopting GNNs in their domains. Thus, it has the potential to impact the successful adoption and use of GNNs in a broad range of fields such as Computer Science, Social Science, Health Informatics, Bioinformatics and Education and Military.