Over the last decade, the numerical simulation of incompressible fluid-structure interaction has been a very active research field and the subject of numerous works. This is due, in particular, to the increasing interest of the research community in the simulation of blood flows in large arteries. In this context, the fluid equations have to be solved in a moving domain and the incompressibility constraint makes the coupling sensitive to the added-mass effect. As a result, the solution procedure has to be designed carefully in order to guarantee efficiency without compromising numerical stability. In this paper, we review some of the coupling schemes recently proposed in the literature. Some numerical results that show the effectiveness of the novel approaches are also presented.