Open-world person re-identification （Re-ID） is a task that the query person may not occur in the gallery set in an agnostic space environment. Compared with the closed-world person Re-ID， open-world Re-ID is seen as a subproblem of image retrieval， and is a more challenging and practical application research. We firstly compare and analyze the different pedestrian datasets and describe the development of existing open-set Re-ID works， the discrepancies between closed- and open-world Re-ID， and the modeling process of open-world Re-ID. Then， we focus on summarizing the research methods of open-world Re-ID， which are data-driven research methods， efficiency-driven research methods and application-driven research methods. Finally， the issues of the research and future directions for open-world Re-ID are discussed.