At present, CCTVs and multifunctional cameras have been well equipped everywhere in our daily lives. However, most of the public sectors especially the department of public safety are still using the traditional approach, analysing these data by humans. This research presents a summary of the current technologies and algorithms based on deep learning in person Re-identification (Re-id), which aims to recognize a particular individual in several camera views. This paper firstly described the current challenges in using deep learning for person Re-id. Then, a brief introduction of standard person Re-id including feature learning and metric learning is given. Furthermore, the open world Re-id problem is examined from three aspects: person re-id with occlusions, unsupervised learning-based method, and cross-modal person re-Id. The author then evaluated the regularly used datasets and analysed the performance of the algorithms from recent times. Finally, some potential future directions of research for Re-id are proposed.