The surveillance of large sea areas normally requires the analysis of large volumes of heterogeneous, multidimensional and dynamic sensor data, in order to improve vessel traffic safety, maritime security and to protect the environment. Early detection of conflict situations at sea provides critical time to take appropriate action with, possibly before potential problems occur. In order to provide an overview of the state‐of‐the‐art of research carried out for the analysis of maritime data for situational awareness, this study presents a review of maritime anomaly detection. The found articles are categorized into four groups (a) data, (b) methods, (c) systems, and (d) user aspects. We present a comprehensive summary of the works found in each category, and finally, outline possible paths of investigation and challenges for maritime anomaly detection.