Many natural and engineering flows display self-sustained oscillations in the laminar and turbulent regimes, canonically represented by the Bénard-von Kàrman vortex shedding phenomenon. In the present talk, I will discuss a number of configurations of practical interest where the flow dynamics can be rationalized using basic concepts of local and global linear stability theory, leading to a simple and unified description of their behavior. In particular, I will present results on the controlled injection of gaseous jets in co-flowing liquids and liquid jets either into air or into another co-flowing immiscible liquid. Depending on the values of the governing parameters, these flows may be globally stable or globally unstable, leading to qualitatively different nonlinear regimes, while their fragmentation leads to the formation of bubbles or droplets whose monodispersity depends on the local or global nature of the linear instability. Self-sustained oscillations in submerged jets, wakes behind axisymmetric bluff bodies and diffusion flames will also be discussed in the light of linear stability concepts.