An efficient and effective person re-identification (ReID) system relieves the users from painful and boring video watching and accelerates the process of video analysis. Recently, with the explosive demands of practical applications, a lot of research efforts have been dedicated to heterogeneous person re-identification (Hetero-ReID). In this paper, we provide a comprehensive review of state-of-the-art Hetero-ReID methods that address the challenge of inter-modality discrepancies. According to the application scenario, we classify the methods into four categories --- low-resolution, infrared, sketch, and text. We begin with an introduction of ReID, and make a comparison between Homogeneous ReID (Homo-ReID) and Hetero-ReID tasks. Then, we describe and compare existing datasets for performing evaluations, and survey the models that have been widely employed in Hetero-ReID. We also summarize and compare the representative approaches from two perspectives, i.e., the application scenario and the learning pipeline. We conclude by a discussion of some future research directions. Follow-up updates are available at https://github.com/lightChaserX/Awesome-Hetero-reID