Space debris generated by human space exploration activities has become a major pollutant in space, and also an obstacle and a threat to the development of human space industry. Active space debris removal problem has attracted widespread attention from the international community. Based on the systematic analysis of related domestic and international literature, we briefly introduce the current status of active space debris removal; describe the low earth orbit(LEO) and geosynchronous orbit(GEO) space debris active removal mission planning problem; introduce the planning model from three levels: target selecting and grouping, visiting sequence planning and transfer trajectory planning; categorize and summarize the current literature by explicit enumeration, implicit enumeration, and meta-heuristic methods and analyze the current drawbacks; and finally address the perspective of the space debris active removal planning problem.