Structural vibrations in Tip-Tilt modes usually affect the closed-loop performance of astronomically optical telescopes. In this paper, the state of art control methods—proportional integral (PI) control, linear quadratic Gaussian (LQG) control, disturbance feed forward (DFF) control, and disturbance observer control (DOBC) of Tip-Tilt mirror to reject vibrations are first reviewed, and then compared systematically and comprehensively. Some mathematical transformations allow PI, LQG, DFF, and DOBC to be described in a uniform framework of sensitivity function that expresses their advantages and disadvantages. In essence, feed forward control based-inverse model is the main idea of current techniques, which is dependent on accuracies of models in terms of Tip-Tilt mirror and vibrations. DOBC can relax dependences on accuracy model, and therefore this survey concentrates on concise tutorials of this method with clear descriptions of their features in the control area of disturbance rejections. Its applications in various conditions are reviewed with emphasis on the effectiveness. Finally, the open problems, challenges and research prospects of DOBC of Tip-Tilt mirror are discussed.