In recent years, due to unmanned aerial vehicles (UAV) characteristics such as flexibility, intelligence, and autonomy, UAV has been widely used in military and civilian applications, especially the primary target tracking task in search and surveillance. However, due to the complexity of the scene environment and the variability of the moving targets in UAV visual target tracking, it is difficult to extract features and formulate a model for the target, bringing a significant challenge to the tracking performance. Therefore, we provide a review of UAV visual target tracking. First, we present the current state of researching visual target tracking, review the classical and latest tracking algorithms, especially those based on correlation filtering and deep learning, and compare the advantages and disadvantages of different algorithms. Then, we summarize the commonly-used UAV target tracking datasets and evaluation metrics. Finally, we present a prospect of the future directions for developing UAV visual target tracking algorithms.