Bioinspired vision sensors have become very attractive in recent years because of their inherent redundancy suppression, integrated processing, fast sensing capability, wide dynamic range, and low power consumption. These sensors combine functionalities of the biological “where” and “what” systems of the human visual system and process the visual information using an asynchronous event-driven method. Since the emergence of bioinspired vision sensors, various applications based on them have been proposed in the computer vision and robotics fields. In this paper, we review bioinspired vision sensors and their applications. The reviewed sensors include dynamic vision sensors (DVSs), asynchronous time-based image sensors (ATISs), and dynamic and active pixel vision sensors (DAVISs). The reviewed applications based on the bioinspired vision sensors include visual tracking, detection, recognition, simultaneous localization and mapping (SLAM), reconstruction, stereo matching, and control.