[PIEEE, 2024] This paper discusses the growing relevance of graph neural networks (GNNs) across various real-world applications, from recommendation systems to drug discovery, emphasizing the need for trustworthy GNNs beyond task performance. The survey proposes a comprehensive roadmap for building such GNNs, addressing six key aspects: robustness, explainability, privacy, fairness, accountability, and environmental well-being. Additionally, it highlights the interrelations among these aspects and presents future directions for advancing trustworthy GNN research and its industrial applications.