Bearings, gears, harmonic resonators of gyroscopes, and mirrors are the core basic components to realize rotation support, power transmission, attitude control, and space exploration of spacecraft. They directly affect the performance, life, and reliability of spacecraft. To ensure the smooth progress of space missions, the basic components of spacecraft must possess excellent service performance, high reliability, and long service life. The state of the working surfaces is the key influencing factor. Therefore, the accuracy and surface quality of the working surfaces must be continuously improved from the manufacturing perspective. However, most of the working surfaces of basic components of spacecraft are complex and curved, and the materials contain various elements and metallographic structures. Therefore, it is difficult to achieve consistent and controllable polishing. Based on the characteristics of bearings, gears, harmonic resonators of gyroscopes, and mirrors, this work briefly stated the demand and necessity of ultra-precision polishing, classified and summarized the existing ultra-precision polishing technologies, such as lapping and chemical mechanical polishing, electrochemical mechanical polishing, and rheological polishing applied to bearings, abrasive flow polishing, rheological polishing, and electrochemical mechanical polishing applied to gears, rheological polishing, femtosecond laser balancing, and ion beam balancing applied to gyroscope resonators, magnetorheological polishing, computer controlled optical surfacing, bonnet polishing, and ion beam figuring and polishing applied to mirrors, described their polishing principles and performance, and finally briefly prospected the future development, so as to provide a reference for ultra-precision machining of basic components of spacecraft.