With the explosive growth of current data volume and the rapid development of big data technology, mining valuable information from massive data has become a crucial task. As one of the key tasks in the field of data mining, anomaly detection plays a vital role in many fields such as industrial system monitoring, medical diagnosis, communication security, and financial fraud detection. In view of the diverse characteristics of big data, the data types processed by anomaly detection are far from being covered by a single time series. It may also include multi-modal data types such as network data and spatiotemporal series. This article aims to systematically summarize and in-depth sort out anomaly detection technologies applied to different types of data, with a view to providing reference and guidance for researchers and practitioners in related fields.