To what extent do migrants carry their culture with them, and to what extent do they acquire the culture of their new home? The answer not only has important political implications; it also helps us understand the extent to which basic cultural values are enduring or malleable, and whether cultural values are traits of individuals or are attributes of a given society. The first part of this article considers theories about the impact of growing social diversity in Western nations. We classify two categories of society: Origins (defined as Islamic Countries of Origin for Muslim migrants, including twenty nations with plurality Muslim populations) and Destinations (defined as Western Countries of Destination for Muslim migrants, including 22 OECD member states with Protestant or Roman Catholic majority populations). Using this framework, we demonstrate that, on average, the basic social values of Muslim migrants fall roughly midway between those prevailing in their country of origin and their country of destination. We conclude that Muslim migrants do not move to Western countries with rigidly fixed attitudes; instead, they gradually absorb much of the host culture, as assimilation theories suggest.