Abstract
Ever since Matsuno's pioneering numerical simulations of the stratospheric sudden warming there has been little reason to doubt that this spectacular natural phenomenon is essentially dynamical in origin. But theoretical modelling, and the use of satellite observations, are only just reaching the stage where there seem to be prospects of understanding stratospheric warmings in some detail and forecasting them reasonably well. An informal discussion of recent progress is given, and suggestions are made for future work, including a way of avoiding spurious resonances in mechanistic numerical models in which tropospheric motions are prescribed a priori.