This paper is written under the materials of the Round Table 'Rigid Body Dy
namics: Past, Present, Future' which was held at the International Conferen
ce on 'Stability, Control and Rigid Bodies Dynamics' in Donetsk, September
8, 1999. The paper includes the speeches of the discussion participants as
well as an analysis of the results obtained in rigid body dynamics in 20th
century. The priority directions in the future development of rigid body dy
namics are proposed.