A thermomechanical processing (TMP) structure map is proposed that plots the critical strains required for dynamic recrystallization along with the grain sizes that result. These maps are useful in identifying the limits to grain refinement and designing hot working processes. They are readily constructed for well studied alloys such as plain carbon steel. In light of the recent interest in the hot working of magnesium, initial steps are taken here to construct a TMP structure map for the most common wrought magnesium alloy, AZ31. The completion of dynamic recrystallization is estimated using a geometrical approach and a twinning region is identified.