Superplastic forming (SPF) of magnesium alloys has received increasing attention in the recent past. The aim of this presentation is to review recent works dealing with SPF of Mg alloys with a three-fold objective: i. How to produce fine or ultra fine grained (UFG) microstructures? ii. Are there specifities in superplastic deformation mechanisms? iii. How SPF Mg alloys resist to cavitation? Deformation mechanisms as well as damage variations in the superplastic regime will be preferentially discussed in relation with grain size, content in intermetallic particles and diffusion kinetics. For the sake of illustration, some results concerning the superplastic behaviour of UFG magnesium alloys produced by severe plastic deformation will be presented since such microstructures exhibit particularly attractive superplastic properties at quite low temperatures.