Abstract. Automatic anomaly detection is of great importance in industry, remote sensing, and medicine. It is important to be able to automatically process large amounts of data to detect, for example, chemical objects in multispectral and hyperspectral satellite images, sea mines in side-scan sonar images, or defects in industrial monitoring applications. Automatic detection of anomalous structures on arbitrary images refers to the task of finding inappropriate patterns relative to the normal state of the image. This is a difficult task in computer vision, since there is no clear and straightforward definition of what is normal or not normal for a given arbitrary image. The practical importance is manifested in the development of algorithms and models that can automatically detect unusual or anomalous patterns in images. An analysis of methods for finding anomalies in images from the point of view of the possibility of application to arbitrary images has been carried out. The classification of anomaly detection methods according to the criteria of the involved approaches and models used for modeling the background is presented. Methods that use machine learning, such as one-class support vector method and variational autoencoder, nearest neighbor-based anomaly detection, clustering-based anomaly detection, statistical anomaly detection, spectral anomaly detection, anomaly detection using information theory are discussed. The main attention is paid to the methods classified according to the background modeling approach. Five categories of background modeling methods based on probability density function, global and local homogeneity, sparsity, and self-similarity are considered. For anomaly detection applications, it is recommended to use methods in which the background model best describes the expected anomaly-free background, as this generally results in the best performance. On the basis of research, it was established that an effective universal model for detecting anomalies in arbitrary images should: use only a self-similar or sparse background model; process the residual image as a stochastic process to detect anomalies, such as anomalies in color noise; preprocess the residual image before detecting the anomaly.