Rapidly pulsating Ap stars present the widest range of physical phenomena in any pulsating star. It seems probable that most of the driving is due to the κ mechanism in the H ionization zone in which convection is suppressed by the magnetic eld. Recent attempts to model some stars show that driving by this mechanism is sometimes insu cient and that another unknown mechanism is also at work. This is also indicated by the fact that the predicted instability strip for the κ mechanism is much hotter than observed. Much progress has occurred in the last decade and we now have a good understanding of the cyclic frequency jumps that occur in models as the magnetic eld is changed. Coupling of the pulsation with the magnetic eld induces a slow wave which is thought to damp δ Scuti pulsations in these stars. However, recent space observations have shown that in at least one roAp star a low frequency mode is also present, presenting a challenge to this idea. The eigenfunctions are far from simple spherical harmonics, considerably complicating mode identi cation. Observations indicate the presence of pulsational nodes in the atmosphere and variations in amplitude and phase shifts between di erent atomic species. This appears to be the result of chemical strati cation and running waves. The line pro le variations are axisymmetric except in the uppermost atmospheric layers. The non-axisymmetric variations are not understood, but may be a result of turbulence in the atmosphere or shock waves.