Abstract: In 1959, the former Soviet Union's lunar mission Luna-1pioneered the man's deep space exploration activity. More than180 deep space spacecrafts have been launched so far. All large celestialbodies in the solar system including the sun itself were explored. The firstboom of deep space exploration occurred in the 60\sim70's of the last century, andafter a short period of inactiveity in the 1980s, the internationalspace community has seen its second boom from the 1990s, with newideas and new technologies for the deep space missions.From the point of view of the mission design, theyinvolve many basic problems of dynamics and control. This paperpresents recent development and challenge of the fundamental dynamics andcontrol problems with respect to the deep space mission design.