The rapid advancement of sensor technology has resulted in a vast volume of traffic trajectory data, and trajectory anomaly detection has a wide range of applications in sectors including smart transportation, autonomous driving, and video surveillance. Trajectory anomaly detection, unlike other trajectory mining tasks like classification, clustering, and prediction, tries to find low-probability, uncertain, and unusual trajectory behavior. The types of anomalies, trajectory data labels, detection accuracy, and computational complexity are all frequent issues in trajectory anomaly detection. In view of the above problems, the research status and latest progress of trajectory anomaly detection technology in the past two decades are comprehensively reviewed. First, the characteristics of trajectory anomaly detection and the current research challenges are analyzed. Then, the existing trajectory anomaly detection algorithms are compared and analyzed based on the classification criteria such as the availability of trajectory labels, the principle of anomaly detection algorithms, and the working mode of offline or online algorithms. For each type of anomaly detection technology, the algorithm principle, representative method, complexity analysis and algorithm advantages and disadvantages are summarized and analyzed in detail. Then, the open source trajectory datasets, commonly used anomaly detection evaluation methods and anomaly detection tools are discussed. On this basis, the architecture of the trajectory anomaly detection system is presented, and a series of relatively complete trajectory mining processes from trajectory data collection to anomaly detection application are formed. Finally, the significant open issues in the domain of trajectory anomaly detection are discussed, as well as potential research trends and solutions.