The maritime domain is the most utilised environment for bulk transportation, making maritime safety and security an important concern. A major aspect of maritime safety and security is maritime situational awareness. To achieve effective maritime situational awareness, recently many efforts have been made in automatic anomalous maritime vessel movement behaviour detection based on movement data provided by the Automatic Identification System (AIS). In this paper we present a review of state-of-the-art automatic anomalous maritime vessel behaviour detection techniques based on AIS movement data. First, we categorise some approaches proposed in the period 2011 to 2016 to automatically detect anomalous maritime vessel behaviour into distinct categories including statistical, machine learning and data mining, and provide an overview of them. Then we discuss some issues related to the proposed approaches and identify the trend in automatic detection of anomalous maritime vessel behaviour.