The development of reliable H-modes on MAST, together with advances in heating power and a range of high spatial resolution diagnostics, has provided a platform to enable MAST to address some of the most important issues of tokamak stability. In particular the high β potential of the spherical tokamak is highlighted with stable operation at βN ∼ 5–6, βT ∼ 16% and βp up to ∼2. Magnetic diagnostic evaluation of the global β parameters is independently confirmed by kinetic profile data. Calculations indicate that the βN values are in the vicinity of no-wall stability limits. Studies of neoclassical tearing modes (NTMs) have been extended to explore their effects and develop avoidance strategies. Experiments have demonstrated that sawteeth play a strong role in triggering NTMs—by avoiding large sawteeth a much higher βN value has been reached. The significance of NTMs is confirmed, with large islands observed using the 300 point Thomson scattering diagnostic, and locking of large n = 1 modes frequently leading to disruptions, which become more rapid at low q95. The role of error fields has been explored. H-mode plasmas are also limited by edge localized modes (ELMs), with confinement degraded as the ELM frequency rises. However, in contrast to the conventional tokamak, the ELMs in high performing regimes on MAST (HIPB98Y2 ∼ 1) appear to be type III in nature. Modelling using the ELITE code, which incorporates finite n corrections, identifies instability to peeling modes, consistent with a type III interpretation. It also shows considerable scope to raise pressure gradients before ballooning type modes (perhaps associated with type I ELMs) occur. The calculations show that narrow pedestals can support much stronger pressure gradients than might be expected from simple n = ∞ ballooning calculations. Finally sawteeth are shown to degrade confinement by ∼10–15% in particular cases examined. They are observed not to remove the q = 1 surface in the cases where snakes are present—various physics models of the sawteeth are now being explored. Thus research on MAST is not only demonstrating stable operation at high performance levels and developing methods to control instabilities; it is also providing detailed tests of the stability physics and models applicable to conventional tokamaks, such as ITER.