In recent decades, the emphasis on renewable resources has grown considerably, leading to significant advances in the sector of wave energy. Nevertheless, the market cannot still be considered as commercialized, as there are still other obstacles in the mooring system for wave energy converters (WECs). The mooring system must be designed to not negatively impact the WEC’s efficiency and reduce the mooring loads. Firstly, the overview of the types of wave energy converters (WECs) are classified through operational principle, absorbing wave direction, location, and power take-off, respectively, and the power production analysis and design challenges of WECs are summarized. Then, the mooring materials, configurations, requirements, and the modeling approaches for WECs are introduced. Finally, the design of mooring systems, including the design considerations and standards, analysis models, software, current research focus, and challenges are discussed.