The authors consider the history of Computer Algebra (CA) development and applications at the famous Keldysh Institute of Applied Mathematics (Russia Academy of Science). At the Institute CA was used in various areas: Applied Celestial Mechanics, Mathematics, Robotics, Hydromechanics, and Methods of Calculation. Authors compared and classified the existing systems and their possibilities. An attention is paid to REFAL (REcursive Functions Algorithmic Language), developed in the Institute. The modern state of investigations is also concerned. The list of the main references is presented.