In this talk I present some recent advances on the discretization of fluid-structure interaction problems based on the Lagrange multiplier formulation. The problem fits in the framework of saddle point systems, so that possible choices of the finite element spaces have been investigated recently. Our formulation allows for solving the Navier-Stokes equation and the elasticity equation on meshes independent of each other, at the price of computing a coupling term which involves test funtions defined on both meshes. A discussion on how to deal carefully with such term will also be presented.