The fluid-structure interaction (FSI) problem plays significant roles in engineering simulations and design. This problem considers the interaction between the fluid domain and structural domain with one-way or two-way data transfer. There are several algorithms to solve the problem, mainly numerical duo to the complexity and nonlinearly. The numerical schemes focus on the modeling method of the coupling interface. However, there are several algorithms that merge the interface in the equations and deal with the domains as a unified set of equations. Future development could include artificial intelligence modeling and the inclusion of more physical domains into the systems.