The fuel cell hybrid electric vehicle (FCHEV) with a fusion of multiple energy sources can make up for the shortcomings of the pure fuel cell vehicle. Nevertheless, multiple energy sources increase the complexity of the operating mode of the power system. Therefore, how to make multiple energy sources operate efficiently, stably and reliably has become one of the critical technologies for the FCHEV. In this paper, a systematic classification of FCHEV’s topologies is introduced, and the characteristic of various topologies is discussed. Then, a comparative analysis of energy management strategies (EMSs) of the FCHEV, including rule-based, optimization-based, and advanced learning-based EMSs, is presented. Finally, according to the different characteristics of topologies and EMSs, the fuel cell energy management research in the last decade is summarized and the development trend of EMSs is further analyzed by the statistical analysis method. On this basis, the current challenges and advancement trends of EMSs are summarized, which is instructive for researchers working on EMS.