Person re-identification (ReID) plays a crucial role in video surveillance with the aim to search a specific person across disjoint cameras, and it has progressed notably in recent years. However, visible cameras may not be able to record enough information about the pedestrian’s appearance under the condition of low illumination. On the contrary, thermal infrared images can significantly mitigate this issue. To this end, combining visible images with infrared images is a natural trend, and are considerably heterogeneous modalities. Some attempts have recently been contributed to visible-infrared person re-identification (VI-ReID). This paper provides a complete overview of current VI-ReID approaches that employ deep learning algorithms. To align with the practical application scenarios, we first propose a new testing setting and systematically evaluate state-of-the-art methods based on our new setting. Then, we compare ReID with VI-ReID in three aspects, including data composition, challenges, and performance. According to the summary of previous work, we classify the existing methods into two categories. Additionally, we elaborate on frequently used datasets and metrics for performance evaluation. We give insights on the historical development and conclude the limitations of off-the-shelf methods. We finally discuss the future directions of VI-ReID that the community should further address.