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Person re-identification (re-ID) has become increasingly popular in the community due to its application and research significance. It aims at spotting a person of interest in other cameras. In the early days, hand-crafted algorithms and small-scale evaluation were predominantly reported. Recent years have witnessed the emergence of large-scale datasets and deep learning systems which make use of large data volumes. Considering different tasks, we classify most current re-ID methods into two classes, i.e., image-based and video-based; in both tasks, hand-crafted and deep learning systems will be reviewed. Moreover, two new re-ID tasks which are much closer to real-world applications are described and discussed, i.e., end-to-end re-ID and fast re-ID in very large galleries. This paper: 1) introduces the history of person re-ID and its relationship with image classification and instance retrieval; 2) surveys a broad selection of the hand-crafted systems and the large-scale methods in both image- and video-based re-ID; 3) describes critical future directions in end-to-end re-ID and fast retrieval in large galleries; and 4) finally briefs some important yet under-developed issues.