Graph Anomaly Detection is a crucial task for identifying abnormal patterns in graph-structured data, also known as networks, which represents the interactions between real-world objects. It has a wide range of applications in cybersecurity, fault detection, and social network analysis. Detecting anomalies in graphs requires considering both topological and contextual information in large-scale, complex, high-dimensional graphs. This thesis develops novel, scalable, and high-performance deep learning methods for graph anomaly detection under various application settings. Our work advances research in this field and provides effective tools to address critical real-world problems in large-scale networks.