An elaborated overview of current research and development in multiple extended object tracking based on the random finite set method is provided. A clear definition and mathematic model of the extended object is given. Then, three shape estimation methods of the extend object including the random matrix, random hypersurface and gaussian process are provided. Then, the algorithms of the random finite set filter of the multiple extended object are given. Finally, the advantage and disadvantage of the tracking algorithm are presented, and current applications and further research prospects are also introduced in the conclusion.