The relationships to Islam of the many Christians who lived in Muslim lands, for example, were very different from those of Christians living in orthodox Christian Byzantium or Catholic Latin Europe. This chapter focusses on those lands that came to think of themselves as 'Christendom': that is, Catholic Western Europe, from the Iberian to the Hungarian kingdoms. The actual content of the Saracens' faith was irrelevant to Sophronios, who was interested in elucidating the Muslims' role in Christian sacred history. Engagement with Islamic texts did not alter Christian understandings of Islam because this engagement was largely structured by polemic. Iberian Muslims living under Christian rule are called 'Mudejars', and they represent a novel and important phenomenon in Islamic history. Certainly most Mudejar scholars felt that theirs was a culture in decline. The importance of polemics to Muslims living within Christendom reminds us of my earlier conclusions about Christian encounters with Islam.