This publication is dedicated to mathematical and numerical models for fluid-structure interaction. This concerns the study of mechanical systems involving a fluid and a structure that have a mechanical influence on each other. This book focuses in particular on unsteady aeroelasticity. At the beginning of this new millenium, aeroelasticity is a meeting point between the well-developed theories of unsteady aeroelasticity, and the recently developed and still immature methods for unsteady flow calculations. The Euler model is now standard, the unsteady Navier-Stokes model is the new challenge. In the next few years, progress in aeroelasticity will be heavily dependent on the improvement in simulation tools for unsteady turbulent flows, especially those involving large vortices. The content of this publication is devoted to a major extent to theoretical issues, with the first chapter proposing a review of recent results in energy estimates and the existence of continuous solutions. A number of chapters focus on the recent design of efficient numerical strategies as the result of theoretical advances. The last three chapters describe recent applications of a 3D unsteady numerical model.