The theory of supposition with the associated theories of copulatio, ampliatio and distributio constitute one of the most original achievements of Western medieval logic. The twelfth century produced a considerable harvest of rules about the referential range of terms in various contexts. This chapter explains some characteristic features of twelfth- and early thirteenth-century speculation about supposition without going into details and without paying much attention to the opinions of individual authors. De Rijk starts by considering some passages in Priscian. The discussion of sophisms was a legacy from the days before the arrival of the Logica Nova. But the business was still flourishing, at least in England, towards the middle of the thirteenth century. There is evidence that medieval logicians thought that was what they had the theory of supposition for, and there is ample evidence that they used it to solve sophisms. The decline of the theory of supposition coincides with important changes in logical theory and teaching.