Graph anomaly detection has attracted a lot of interest because its important uses in social network analysis, fraud detection, cybersecurity, and healthcare. Modern approaches and applications in graph-based anomaly detection are comprehensively reviewed in this work. Emphasizing their relevance across various graph types—static, dynamic, attributed, and heterogeneous graphs—it classifies anomalies into node, edge, subgraph, and graph-level abnormalities. We review conventional statistics and distance-based approaches first, then we look at machine learning models including semi-supervised, unsupervised, and supervised learning. Advanced deep learning techniques—Graph Neural Networks (GNNs), autoencoders, and temporal models—which show exceptional performance in complicated graph structures—are also explored in the survey. Applications covered in several spheres, including cybersecurity for intrusion detection, financial fraud detection, social network analysis for bogus account identification, and healthcare anomaly detection. Additionally included are benchmark datasets and evaluation measures necessary for performance evaluation. Including explainable AI, self-supervised learning, cross-domain anomaly detection, and federated learning, the survey ends with addressing current issues including scalability, interpretability, and data imbalance and points future research paths. This extensive poll seeks to be a useful tool for practitioners and academics advancing graph-based anomaly detection methods.