The existence in nuclei of a stable superdeformed shape at high spin has been well established. The increasing number of examples has shown variations in the properties of the superdeformed bands. As each new feature has been explained invariably the next observation has highlighted a new phenomena. The net result has been a rapidly evolving subject which has dramatically increased our understanding of rapidly rotating nuclei. However, the experimentalists are now clearly limited by the efficiency and sensitivity of the current generation of γ-ray arrays. Over the next few years there is the prospect of new spectrometers (GAMMASPHERE in the USA, EUROGAM and EUROBALL in Europe) which will lower the limit of observation of weak cascades by two orders of magnitude. These instruments will clearly give a major new impetus to high spin γ-ray spectroscopy and we can expect even more new discoveries. The results and ideas reviewed in this talk are the fruits of the labours of many colleagues, both experimental and theoretical, from groups in many countries. I gratefully acknowledge many discussions and the use of data before publication. The data on 152Dy, 151Tb, 150Gd and 142Eu were derived from experiments at Daresbury and the analysis was due to P. Fallon, A. Alderson, I. Ali, G. Smith and S. Mullins and D.M. Cullen. The support of the U.K. Science and Engineering Research Council is gratefully acknowledged.