During the lifetime of the Acoustical Society of America, certain developments have led to an improved understanding of the physical and tonal properties of woodwind instruments. These developments include theoretical analysis, instrumentation for measuring acoustical properties, and high speed digital computing. This paper will review past work, summarize the present state of our knowledge. and offer some conjectures on the future. The content is restricted to a consideration of mechanical‐reed woodwinds, although comparable things could be said about “air‐reed” woodwinds. The following aspects will be discussed: (1) acceptable bore shapes; (2) theory of tone holes; (3) experimental measurement of input impedance: (4) numerical calculation of input impedance; (5) implications of input impedance: (6) reed and air‐column interaction: (7) small‐amplitude, steady‐state vibrations: (8) medium‐amplitude, nonbeating, steady‐state vibrations; (9) functional modeling of arbitrary amplitude transient and steady‐state vibrations: (10) tonal analysis‐synthesis and spectral properties; and (11) tonal perception.