This survey provides a comprehensive overview of the state-of-the-art methods for anomaly detection in graph data. It highlights the importance of considering the inter-dependent nature of data objects in graphs, which is crucial for effective anomaly detection. The survey categorizes the methods into unsupervised and (semi-)supervised approaches, for static and dynamic graphs, and for attributed and plain graphs. Key aspects such as effectiveness, scalability, generality, and robustness are discussed, along with the importance of anomaly attribution for further analysis. Real-world applications in various domains, including finance, auction, computer traffic, and social networks, are presented. The survey concludes with a discussion on open theoretical and practical challenges in the field.This survey provides a comprehensive overview of the state-of-the-art methods for anomaly detection in graph data. It highlights the importance of considering the inter-dependent nature of data objects in graphs, which is crucial for effective anomaly detection. The survey categorizes the methods into unsupervised and (semi-)supervised approaches, for static and dynamic graphs, and for attributed and plain graphs. Key aspects such as effectiveness, scalability, generality, and robustness are discussed, along with the importance of anomaly attribution for further analysis. Real-world applications in various domains, including finance, auction, computer traffic, and social networks, are presented. The survey concludes with a discussion on open theoretical and practical challenges in the field.