Space is the driving force of the world’s sustainable development, and ensuring the sustainability of human activity in space is also necessary. Robotic arm active debris capture removal (RA-ADCR) is a noteworthy technology for containing the dramatic increase in space debris and maintaining orbital safety. This review divides the RA-ADCR technology progress history into three periods and presents the status of related research. Two major development trends are summarized and subdivided through the analysis and collation of research achievements over the past three years. Taking the treatment of parameter uncertainties as the entry point, researchers would like to improve the discrimination accuracy and scope to reduce uncertainties. On the other hand, researchers accept such uncertainties and would like to offset and avoid the impact of uncertainties by extending the error margins. Subsequently, the challenges of RA-ADCR are analyzed in line with the task execution flow, which mainly focuses on the conflict between on-satellite computing power and the performance of task execution. In addition, feasible solutions for the current phase are discussed. Finally, future outlooks are evaluated and discussed.