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Several algorithms for fluid-structure interaction are described. All of them are useful for the loose coupling of fluid and structural dynamics codes. The first class of algorithms considers the loose coupling of implicit time-marching codes. Of these, a predictor-corrector algorithm that may be interpreted as a Jacobi iteration with block-diagonal terms was found to be a good compromise of simplicity, generality and speed. The second class of algorithms treats the displacement of the surface of the structure that is in contact with the fluid. It is shown that a straightforward treatment of the displacements for arbitrary choice of timesteps can lead to instabilities. For optimal stability, at each timestep the ending time of the fluid should be just beyond the ending time of the structure. The third class of algorithms treats the movement of the flow mesh in an ALE setting. The use of a projective prediction of mesh velocities, as well as linelet preconditioning for the resulting PCG system can reduce significantly the effort required. Examples are included that show the effectiveness of the proposed procedures. [ABSTRACT FROM AUTHOR]