The theory of coronal structure and of the associated angular momentum transport by magneto-thermo-centrifugal winds is reviewed, with reference to recent observations of rapidly rotating late-type stars. In particular, the combined optical and X-ray studies of AB Doradus are consistent with the predicted picture of a hot, magnetically-controlled ‘dead zone’ in near corotation with the star, and of cooler wind-emitting regions (analogues of the solar coronal holes). The standard theory predicts a rate of angular momentum transport that depends on the extent of the wind zone, the relative importance of thermal and centrifugal driving, and the variation of the dynamo-built surface field with rotation. For stars like the Sun, with approximately one tenth of the mass in the convective envelope, detailed comparison of the theory with the observed rotations of stars in clusters of different ages is sensitive to the strength of the coupling between the envelope and the radiative core, and is constrained by helioseismological limitations on rotational shear within the present-day Sun. An inferred strong braking during the early epochs may hint at a non-standard braking model, with the Maxwell stresses dominant far from as well as near the stellar surface.