Sawtooth oscillations were first discovered on the ST tokamak and were reported in 1974 by von Goeler, Stodiek and Sauthoff. These oscillations are now seen regularly on all tokamaks and can be observed on many diagnostics including soft X-ray, temperature and density measurements. The basic pattern consists of a slow increase in central temperature and density brought to an end by a sudden collapse, the whole process repeating in a periodic manner. Outside the central region an inverted sawtooth is seen, a slow decay being followed by a fast rise. The theory of these oscillations has had a fascinating but rather contorted development. It would be satisfying if it were possible to say that this development had led us to an understanding of the subject but unfortunately the present state is one of mystery. However it could be argued that this makes a review of the subject more useful. This talk will be in three parts. The first will sketch the historical development of the subject. The second will describe the more recent work and particularly that relating to JET. The third will review the problems which the experimental results pose for proposed theoretical explanations.