This paper presents an outline of the sound production mechanisms in wind instruments and reviews recent progress in the research on different types of wind instruments, i.e., reed woodwinds, brass, and air-jet driven instruments. Until recently, sound production has been explained by models composed of lumped elements, each of which is often assumed to have only a few degrees of freedom. Although these models have achieved great success in understanding the fundamental properties of the instruments, recent experiments using elaborate methods of measurement, such as visualization, have revealed phenomena that cannot be explained by such models. To advance our understanding, more minute models with a large degree of freedom should be constructed as necessary. The following three different phenomena may be involved in sound production: mechanical oscillation of the reed, fluid dynamics of the airflow, and acoustic resonance of the instrument. Among them, our understanding of fluid dynamics is the most primitive, although it plays a crucial role in linking the sound generator with the acoustic resonator of the instrument. Recent research has also implied that a rigorous treatment of fluid dynamics is necessary for a thorough understanding of the principles of sound production in wind instruments.