The use of machine learning for anomaly detection is a well-studied topic within various application domains. However, the detection problem for market surveillance remains challenging due to the lack of labelled data and the nature of anomalous behaviours, which are often contextual and spread over a sequence of anomalous instances. This paper provides a comprehensive review of state-of-the-art machine learning methods used, particularly in financial market surveillance. We discuss the research challenges and progress in this field, mainly applied in other related application domains. In particular, we present a case of machine learning-based surveillance system design for a physical power trading market and discuss how the nature of input data affects the effectiveness of the methods on detecting anomalous market behaviours. Overall, our findings indicate that the regression tree-based ensemble algorithms robustly and effectively predict day-ahead future prices, showing their capability to detect abnormal price changes.INDEX TERMS Anomaly detection, financial market surveillance, machine learning, time series.