Outer space is an ultimate field for the application of robotics technology. As outer space is a harsh environment with extreme temperatures, vacuum, radiation, gravity, and great distances, human access is very difficult and hazardous and is therefore limited. To assist human activities in space for constructing and maintaining space modules and structures, robotic manipulators have been playing essential roles in orbital operations. Moreover, expanding the horizons of exploration beyond the areas of human access, robots that land and travel on planetary surfaces have been greatly contributing to our knowledge of the solar system. New challenges are expected in the future. This article consists of three parts. In the first part, the achievements of orbital robotics technology in the last decade are reviewed, highlighting the Engineering Test Satellite (ETS-VII) and Orbital Express flight demonstrations. In the second part, some of the selected topics of planetary robotics from the field robotics research point of view are described. Recent achievements in the author's laboratory are added as an illustrative example. Finally, technological challenges to asteroid robotics are discussed. When designing a robot to explore the surface of an asteroid, microgravity raises an interesting problem of how to stick and move on the surface. Some ideas to address these questions are introduced.