Abstract: In order to extend the life of a malfunctioning satellite in orbit, or remove space debris and failed satellites off from the important orbit locations, it is becoming increasingly important to use space robots to take over the control of attitude or/and orbit of space targets. In this paper, various kinds of control methods which can be used for space targets takeover control are systematically investigated. According to the different contact ways with the target, they are divided into rigid takeover control, tethered flexible takeover control and contactless takeover control. All kinds of control methods are described in detail. Finally, the specific principles, operation modes and key technologies of these three kinds of takeover control methods are systematically summarized and analyzed, their respective characteristics, advantages and disadvantages are summarized, and the theoretical and practical research in related fields is prospected.