Fluid-structure interactions are very common in mechanical and civil engineering because many structures, as bridges, offshore risers, transmission lines or wind turbines are directly in contact with a fluid, which can be air, which will be source of wind, or water, which will perturb the structure through waves. An important role of the engineer is to prevent structure failure due to instabilities created by the fluid-structure interactions. This work will first present all the basic concepts needed for the study of fluid-structure interaction problems. Thus, a dimensional analysis of those problems is performed and also all the equations governing such cases are presented. Then, thanks to the dimensional analysis made, a classification of problems, namely based on the reduced velocity, can be done and some conclusions concerning the consequences of the fluid-structure interactions can be drawn in terms of stability or, which is more interesting, instability. Indeed, using simplified models one can show static and dynamic flow-induced instabilities that may be critical for the structure. The final parts of the work will present a specific non-linear structure, a suspension bridge. First the formulation of a simplified one-dimensional model is explained and then, through a finite element discretization, a dynamical study is performed. Also, some conclusions are made concerning the dynamic of suspension bridges. The last part of this work presents a method that was an important source of publication for us, the Smooth Decomposition method.