With increasing human space activities， space missions are evolving towards the need to meet multiple constraints and high performance. Due to the capability in handling constrained optimization problems， the model predictive control （MPC） has been widely studied in spacecraft control in recent years. This paper first reviews the development of MPC and categorizes its applications in spacecraft based on its basic form. Then， considering the uncertainty in space environments， the robust MPC and the stochastic MPC are summarized together with their applications. After that， the safety issues of spacecraft are taken into account and studies on obstacle avoidance and fault-tolerance are discussed in MPC framework. In addition， considering the high computational requirements of MPC， this paper also outlines some efficient methods from the perspectives of control strategy and optimization form， including decentralized/distributed MPC and explicit MPC methods. Finally， in consideration of the actual needs and future development of spacecraft， this paper provides several suggestions for further research on MPC in the spacecraft control aera.