The vertical structure of the tangential wind field in tropical cyclones is investigated through observations, theory, and numerical simulations. First, a dataset of Doppler radar wind swaths obtained from NOAA/AOML/HRD is used to create azimuthal mean tangential wind fields for 7 storms on 17 different days. Three conventional wisdoms of vertical structure are reexamined: the outward slope of the Radius of Maximum Winds (RMW) decreases with increasing intensity, the slope increases with the size of the RMW, and the RMW is a surface of constant absolute angular momentum (M). The slopes of the RMW and of M surfaces are objectively determined. The slopes are found to increase linearly with the size of the low-level RMW, and to be independent of the intensity of the storm. While the RMW is approximately an M surface, M systematically decreases with height along the RMW. The steady-state analytical theory of Emanuel (1986) is shown to make specific predictions regarding the vertical structure of tropical cyclones. It is found that in this model, the slope of the RMW is a linear function of its size and is independent of intensity, and that the RMW is almost exactly an M surface. A simple time-dependent model which is governed by the same assumptions as the analytical theory yields the same results. Idealized hurricane simulations are conducted using the Weather Research and Forecasting (WRF) model. The assumptions of Emanuel's theory, slantwise moist neutrality and thermal wind balance, are both found to be violated. Nevertheless, the vertical structure of the wind field itself is generally well predicted by the theory. The percentage rate at which the winds decay with height is found to be nearly independent of both size and intensity, in agreement with observations and theory. Deviations from this decay profile are shown to be due to gradient wind imbalance. The slope of the RMW increases linearly with its size, but is systematically too large compared to observations. Also in contrast to observations, M generally increases with height along the RMW.