Abstract: The theory and method of multi-source information fusion have acquired plenty of the outcomes in the past 20 years. However the theoretical framework of information fusion is not established up to the present. Recently the finite set statistics (FISST) approach, a special random set method, has been proposed by Mahler. FISST provides a fully unified probabilistic foundation for the major aspects of multi-source information fusion. This paper reviews several main aspects of the random set information fusion research that include the background, the key ideas, the theoretical framework and the applications of FISST. Finally several possible future directions of FISST are discussed.