In this talk we will be concerned primarily withacousticalmethods for estimating vocal tract shapes. These fall into two general categories: (i) methods that estimate the shape from the speech signal and (ii) those that require external measurements. Methods in the first category are based on several tacit assumptions. The validity of these assumptions is not easily tested, and the effects of departures from these assumptions are quite significant, yet difficult to quantify. Of the methods in the second category, the one based on periodically measuring the impulse response at the lips [Sondhi and Gopinath, J. Acoust. Soc. Am.49, 1867–1873 (1971)] will be shown to be potentially the most reliable. This method recovers the cross‐sectional area functions exactly for a lossless vocal tract under the single assumption of plane wave propagation. We will briefly review this method and present evidence that departures from the basic assumptions do not drastically affect the reconstructed shapes. We will also review the algorithms presently available to take account of distributed losses. Finally, we will suggest that much useful information would be gained if the impulse response measurements are made simultaneously with an x‐ray movie of the midsagittal plane.