Fluid-Structure Interaction (FSI) problems, as well as many other coupled multi-field problems, have received much attention in recent years and continue to attract more interest. The main reason is that they are of great relevance to many fields of engineering (civil, mechanical, aerospace, bio, etc.) and applied sciences. Similarly, the development and application of corresponding numerical simulation methodologies have received wide attention over the past decades. Thanks to many advances in computational sciences and computing hardware, the numerical modeling and solution of a difficult subset of such problems that was thought to be unfeasible even five years ago, is either feasible today or will become feasible within the nearby future. In recent years, research in computational FSI has witnessed great progress. However, the field remains an active topic of research with many remaining open problems. Current foci center on the better understanding of various numerical approaches via more rigorous analysis, the generalization of special-purpose solution schemes to comprehensive methodologies, and the maturing of computational technologies that have demonstrated great potential a decade ago to transcend them into numerical assets for the solution of grand challenge FSI problems. Nevertheless, the bar for entering this exciting research field is considerably high. It requires mastering a fair amount of computational fluids or fluid dynamics, linear and/or nonlinear computational solid and/or structural dynamics, time-integration, linear algebra, and parallel computing, among other topics. Textbooks in this general area are either specialized, or tend to cater to specific solution approaches rather than fundamental issues. This latter gap is what this CISM course modestly attempts to address. To this effect, the course brings together experts in the area of computational FSI who will cover complementary aspects of this topic from different perspectives. On the disciplinary side, incompressible and compressible flow regimes and linear and nonlinear structural behaviors will be covered. On the interaction side, all three classes of FSI problems will be discussed: (1) those where the interaction is of short duration and the fluid subsystem is characterized by limited displacements, as in shock and impact problems; (2) those problems where the fluid subsystem is also characterized by limited displacements but the interaction is of longer duration, as in elastoacoustic problems; and (3) those problems where the fluid and structural subsystems have large relative motions and the interaction process is dominated by the flow, as in aeroelasticity problems. The formulations of these problems in the Arbitrary Lagrangian Eulerian (ALE) and purely Eulerian settings will be discussed and contrasted. Various associated semi-discretization and discretization schemes will be covered, and their strengths and weaknesses will be explained. These will include ALE and embedded boundary methods for CFD in the first case, and monolithic and partitioned solution procedures in the second case. To address the issue of CPU intensive parametric problems, the course will also include a few lectures on model order reduction in the context of FSI problems. Participants will be given the opportunity to present a poster covering their interest and contribution to this field. This will enable fostering a collegial discussion and provide the lecturers with an opportunity to tailor their material to address specific applications and concerns.