The space–time fluid–structure interaction (FSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM) have been applied to a wide range of 3D computation of FSI problems, some as early as in 1994 and many with challenging complexities. In this paper, we review these space–time FSI techniques and describe the enhancements introduced recently by the T★AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The aspects of the FSI solution process enhanced include the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation, the fluid–structure interface conditions, the preconditioning techniques used in iterative solution of the linear equation systems, and a contact algorithm protecting the quality of the fluid mechanics mesh between the structural surfaces coming into contact. We present a number of 3D numerical examples computed with these new stabilized space–time FSI (SSTFSI) techniques. Copyright © 2007 John Wiley & Sons, Ltd.