It is a challenge to solve complex fluid-structure interaction (FSI) problems through theoretical derivations, whereas numerical simulation provides an effective solution and is widely applied in naval architecture and marine engineering. Based on grid treatment, FSI methods are classified into the body-fitted grid method, non-body-fitted grid method, overset grid method and particle-based method. The research development of these four types of methods is then reviewed. Both the body-fitted grid method and overset grid method can accurately capture the interface and are suitable for high Reynolds number flow problems, and the former is generally employed when structural deformation is considered, while the latter often works well when considering rigid body motion with complex geometric shapes. The non-body-fitted grid method can avoid the mesh update operation to make calculations simpler, and is widely used in the simulation of flow control, development of underwater flexible bionic vehicles and interference of multi-body motion. The particle-based method plays an increasingly important role in simulating strong nonlinear fluid-structure interaction problems involving severe free surface deformation, slamming, explosion, etc. The properties of different FSI problems determine the applicability of different methods. How to select a suitable numerical method and combine the advantages of various methods to develop novel numerical methods that can handle more challenging problems are important development directions for FSI algorithms.