Aeroacoustics is normally concerned with aircraft noise, where turbulent, high-Reynolds-number flows radiate sound as a small by-product of thrust and lift. Musical wind instruments operate in an almost opposite regime: flows are slow and mostly laminar, and the acoustic field is not a by-product but the dominant driver of the system's dynamics. A wind instrument produces a sustained note not by simple resonance but through a self-sustained limit-cycle oscillation: a nonlinear excitation mechanism is coupled to a passive resonator, and together they convert the player's steady breath pressure into a periodic oscillation entirely through their mutual feedback. Thus, the dynamics, pitch and timbre of the sound produced by these instruments do depend on blowing pressure, but also on the nature of the nonlinear source and the geometry of the bore and bell of the instruments. We have used a variety of numerical and experimental methods to examine the manner in which isolated double-reeds and recorder edges convert a steady energy supply into a self-sustained periodic oscillation via a single linear instability followed by nonlinear saturation. Further, when the amplitude of the acoustic field in the resonator is sufficiently large, flow is generated at the open end of the instruments and it can separate from the edges, leading to amplitude-dependent nonlinear losses. The playability and quality of sound of these instruments is determined to some extent by these phenomena, as well as other nonlinear effects which will also be discussed.