The literature data on the superplastic deformation of high purity yttria stabilised tetragonal zirconia polycrystals is reviewed in detail. It is shown that, based on the existence of a threshold stress, the single mechanism of grain boundary sliding (GBS) accommodated by diffusional processes can explain the superplasticity of these materials over all the ranges of temperature, stress, grain size, and surrounding atmosphere that have been studied. The origin of the threshold stress and its quantitative dependence on temperature and grain size is explained in terms of the segregation of yttrium atoms at the grain boundaries. A new model for GBS accommodated by lattice or grain-boundary diffusion is presented which can explain the transition of the stress exponent from 2 to 1.