Rapid development of artificial intelligence motivates researchers to expand the capabilities of intelligent and autonomous robots. In many robotic applications, robots are required to make planning decisions based on perceptual information to achieve diverse goals in an efficient and effective way. The planning problem has been investigated in active robot vision, in which a robot analyzes its environment and its own state in order to move sensors to obtain more useful information under certain constraints. View planning, which aims to find the best view sequence for a sensor, is one of the most challenging issues in active robot vision. The quality and efficiency of view planning are critical for many robot systems and are influenced by the nature of their tasks, hardware conditions, scanning states, and planning strategies. In this paper, we first summarize some basic concepts of active robot vision, and then review representative work on systems, algorithms and applications from four perspectives: object reconstruction, scene reconstruction, object recognition, and pose estimation. Finally, some potential directions are outlined for future work.