Person re-identification (Re-ID) has attract lots of attention in computer vision, which is of great significance to the development of intelligent security and video surveillance. Currently, most existing methods focus on the person re-identification based on visible light, and have achieved good performance. However, the visible light camera cannot be used normally in the dark night, and the new generation of cameras can automatically switch the mode between infrared and visible settings for 24 hours monitoring. Therefore, some scholars have started to study the RGB-IR cross-modality pedestrian re-identification. This paper introduces the Re-ID and cross-modality Re-ID respectively from the definition, research difficulties, and development status. For RGB-IR cross-modality Re-ID, according to the types of methods, they are divided into three categories: methods based on unified feature models; methods based on metric learning; and methods based on modal transformation. We also describe the corresponding datasets and evaluation protocol. Besides, we analyze and summarize the performance of existing algorithms. Finally, the future development directions of RGB-IR cross-modality Re-ID are summarized.