A review of some representative floating wave energy converter (WEC) projects in the world, including the wave energy capturing technology, development history, main dimensions and tested sea sites is presented. The design essentials of WEC mooring system are discussed and a mooring system design procedure for WEC is proposed, which includes the introduction of related design codes and mooring analysis methods. In the last part, a comprehensive review of mooring system design in the current WECs projects is conducted. Different mooring systems and mooring materials are introduced and discussed. Based on the discussions, recommendations are made for the suitable mooring design according to the WEC's dimensions and working principles. It is shown that the elastic synthetic rope has great potential in the application of WEC mooring system, and the hybrid mooring system could be a good solution for WEC station keeping problem.