This paper reviews the theoretical basis and the state-of-art development of the random finite set, emphasis on the difficulties in application and implementation for multi-target tracking. Firstly, for the single sensor case, several typical approximation techniques based on the random finite set(RFS) are discussed, including probability hypothesis density(PHD), cardinalized PHD(CPHD), multi-target multi-Bernoulli(MeMBer), and generalized labeled multi- Bernoulli(GLMB). The development context of the filters is analyzed, and the problems in implementation with Gaussian mixture(GM) and sequential Monte Carlo(SMC) are studied. Then for the multi-sensor case, the processing method of the multi-sensor spatial registration is introduced, and the application of the RFS filter is studied from two aspects: centralized and distributed fusion. In addition, the difficulties and challenges of the RFS filter in practice are analyzed. Finally, based on the recent researches, some future research directions which need to be focused on for the RFS in multi-target tracking are introduced.