Anomaly detection and localization of visual data, including images and videos, are of great significance in both machine learning academia and applied real-world scenarios. Despite the rapid development of visual anomaly detection techniques in recent years, the interpretations of these black-box models and reasonable explanations of why anomalies can be distinguished out are scarce. This paper provides the first survey concentrated on explainable visual anomaly detection methods. We first introduce the basic background of image-level anomaly detection and video-level anomaly detection, followed by the current explainable approaches for visual anomaly detection. Then, as the main content of this survey, a comprehensive and exhaustive literature review of explainable anomaly detection methods for both images and videos is presented. Finally, we discuss several promising future directions and open problems to explore on the explainability of visual anomaly detection.