This paper proposes a creature behaviour-based pursuit strategy named cyclic pursuit for Spacecraft Formation Flying. Cyclic Pursuit Problem is one of the most popular decentralized control methods. However, the applications in space mission are limited. A comprehensive review of the current studies on the theory of pursuit has been presented, including the fundamental principles and developments of three existing algorithms as well as the solutions based on the characteristics of different kinds of pursuit algorithm. Early-stage applications of cyclic pursuit algorithm (CyPA) have been summarized, the same to its characteristics and advantages. Two applicable simulations of Nonlinear Cyclic Pursuit Algorithm (NlCyPA) have been conducted. In the end, the promising future applicability has been highlighted. Besides, further applications of Cyclic Pursuit in space missions have been proposed.