Underwater optical imaging is essential for exploring the underwater environment to provide information for planning and regulating underwater activities in various underwater applications, such as aquaculture farm observation, underwater topographical survey, and underwater infrastructure monitoring. Thus, there is a need to investigate the underwater imaging process and propose clear and long-range underwater optical imaging methods to fulfill the demands of academia and industry. In this manuscript, we classify the eighteen most commonly used underwater optical imaging methods into two groups regarding the imaging principle, (1) hardware and (2) software-based methods, each with an explanation of the theory, features, and applications. Furthermore, we also discuss the current challenges and future directions for improving the performance of current methods, such as improving the accuracy of underwater image formation model estimation, enlarging the underwater image dataset, proposing comprehensive underwater imaging evaluation metrics, estimating underwater depth and integrating different methods (e.g., hardware- and software-based methods for computational imaging) to promote the imaging performance not only in the laboratory but also in practical underwater scenarios.