This paper provides a comprehensive survey of person re-identification (Re-ID) in both closed-world and open-world settings. It discusses the challenges of Re-ID, including varying viewpoints, low-resolution images, illumination changes, occlusions, and heterogeneous modalities. The paper categorizes Re-ID into closed-world and open-world settings, with the closed-world setting assuming that the query person exists in the gallery set, while the open-world setting is more realistic and faces more complex scenarios. The paper introduces a new baseline (AGW) and a new evaluation metric (mINP) for Re-ID, achieving state-of-the-art performance on multiple datasets. It also discusses important open issues in Re-ID, such as handling noisy annotations, limited labels, and domain shifts. The paper reviews existing methods for closed-world Re-ID, including feature representation learning, deep metric learning, and ranking optimization. It also discusses video-based Re-ID and the challenges of handling video data. The paper concludes that Re-ID is still an unsolved problem, and future research should focus on improving the robustness and generalizability of Re-ID systems.This paper provides a comprehensive survey of person re-identification (Re-ID) in both closed-world and open-world settings. It discusses the challenges of Re-ID, including varying viewpoints, low-resolution images, illumination changes, occlusions, and heterogeneous modalities. The paper categorizes Re-ID into closed-world and open-world settings, with the closed-world setting assuming that the query person exists in the gallery set, while the open-world setting is more realistic and faces more complex scenarios. The paper introduces a new baseline (AGW) and a new evaluation metric (mINP) for Re-ID, achieving state-of-the-art performance on multiple datasets. It also discusses important open issues in Re-ID, such as handling noisy annotations, limited labels, and domain shifts. The paper reviews existing methods for closed-world Re-ID, including feature representation learning, deep metric learning, and ranking optimization. It also discusses video-based Re-ID and the challenges of handling video data. The paper concludes that Re-ID is still an unsolved problem, and future research should focus on improving the robustness and generalizability of Re-ID systems.