Hyperspectral images are high-dimensional datasets comprising hundreds of contiguous spectral bands, enabling detailed analysis of materials and surfaces. Hyperspectral anomaly detection (HAD) refers to the technique of identifying and locating anomalous targets in such data without prior information about a hyperspectral scene or target spectrum. This technology has seen rapid advancements in recent years, with applications in agriculture, defence, military surveillance, and environmental monitoring. Despite this significant progress, existing HAD methods continue to face challenges such as high computational complexity, sensitivity to noise, and limited generalisation across diverse datasets. This study presents a comprehensive comparison of various HAD techniques, categorising them into statistical models, representation-based methods, classical machine learning approaches, and deep learning models. We evaluated these methods across 17 benchmarking datasets using different performance metrics, such as ROC, AUC, and separability map to analyse detection accuracy, computational efficiency, their strengths, limitations, and directions for future research. Our findings highlight that deep learning models achieved the highest detection accuracy, while statistical models demonstrated exceptional speed across all datasets. This survey aims to provide valuable insights for researchers and practitioners working to advance the field of hyperspectral anomaly detection methods.