Fluid–structure interaction is of fundamental importance in many aerospace-engineering applications on account of its manifestation in aeroelasticity, aerothermoelasticity, and heat transfer. This chapter is concerned with the fundamentals of fluid–structure interaction and of computational methods for this class of problems. Both kinematic/dynamic and thermal/thermodynamic interactions are considered. We review the conventional Arbitrary–Lagrangian–Eulerian and three-field formulations to accommodate the motion of the fluid domain. In addition, we focus on the precise interpretation and proper enforcement of interface conditions. Finally, we examine the strength of the kinematic/dynamic and thermal/thermodynamic coupling in fluid–structure-interaction problems and its relation to stability and convergence of numerical solution techniques.