The theory of surface-wave propagation around sharp corners in single-wire transmission lines is developed. Two main topics are studied: radiation loss at corners and radiation patterns of corners. An integral expression is obtained for the transmission loss of a corner, and theoretical curves are computed for the entire range of corner angles from 0° to 180°. The theoretical curves are in good agreement with experimental results obtained by the authors and also with some published results by other investigators. In addition, some new features of acute corners are analysed in some detail. For the radiation patterns of the corners an explicit formula is derived, from which a whole range of radiation patterns is calculated and compared with experimental results. The agreement is shown to be good for corners with obtuse angles.