The stratosphere is that part of the atmosphere which lies between ca. 10 and 50 km above the surface of the Earth and which contains the ozone layer. It is the seat of much interesting behaviour in terms of dynamics, radiation and chemistry, now revealed in detail by observations from modern space instruments, but still not completely understood. Other planetary atmospheres exhibit stratospheric behaviour which in some ways resembles, and in others contrasts sharply with, that of the Earth. In reviewing these topics, this paper describes some key problems that will be addressed by new measurements from space in the near future.