In recent years, the High-Dynamic-Range (HDR) image has gained widespread popularity across various domains, such as the security, multimedia, and biomedical fields, owing to its ability to deliver an authentic visual experience. However, the extensive dynamic range and rich detail in HDR images present challenges in assessing their quality. Therefore, current efforts involve constructing subjective databases and proposing objective quality assessment metrics to achieve an efficient HDR Image Quality Assessment (IQA). Recognizing the absence of a systematic overview of these approaches, this paper provides a comprehensive survey of both subjective and objective HDR IQA methods. Specifically, we review 7 subjective HDR IQA databases and 12 objective HDR IQA metrics. In addition, we conduct a statistical analysis of 9 IQA algorithms, incorporating 3 perceptual mapping functions. Our findings highlight two main areas for improvement. Firstly, the size and diversity of HDR IQA subjective databases should be significantly increased, encompassing a broader range of distortion types. Secondly, objective quality assessment algorithms need to identify more generalizable perceptual mapping approaches and feature extraction methods to enhance their robustness and applicability. Furthermore, this paper aims to serve as a valuable resource for researchers by discussing the limitations of current methodologies and potential research directions in the future.