The event-based camera is a novel bio-inspired vision sensor that efficiently captures scene changes in real-time. Unlike traditional frame-based cameras, event cameras only report triggered pixel-level brightness changes (called events) and outputs asynchronous event streams at microsecond resolution. This type of vision sensor has gradually become a hot topic in the fields of image processing, computer vision, robot perception and state estimation, and neuromorphology. We first describe the basic principles, developmental history, advantages, and challenges of event cameras. Then, three typical event cameras (including the DVS, ATIS and DAVIS) and multiple advanced event cameras are introduced. Next, we review the research on applications of event cameras, including feature extraction, depth estimation, optical flow estimation, intensity image estimation and 3D reconstruction, object recognition and tracking, autonomous localization and pose estimation, visual odometry and SLAM, multi-sensor fusion, and other aspects. Finally, the research progress of the event cameras is summarized and the future development trend is discussed.