Biology can provide biomimetic components and new control principles for robotics. Developing a robot system equipped with bionic eyes is a difficult but exciting task. Researchers have been studying the control mechanisms of bionic eyes for many years and considerable models are available. In this paper, control model and its implementation on robots for bionic eyes are reviewed, which covers saccade, smooth pursuit, vergence, vestibule-ocular reflex (VOR), optokinetic reflex (OKR) and eye-head coordination. What is more, some problems and possible solutions in the field of bionic eyes are discussed and analyzed. This review paper can be used as a guide for researchers to identify potential research problems and solutions of the bionic eyes' motion control.