This paper traces the history of the notion of assimilation in the US and Europe. I argue that it has worked as a cognitive scheme leading to an understanding of migration as the entry of foreigners into the nation. I then examine the making of new boundaries in French society that emphasize categories of race and ethnicity to set French citizens apart from foreign nationals. I question if the focus on ethnic and racial distinctions either expresses the dropping of the assimilation paradigm, or allows its preservation by adjusting its meaning to the new configuration. I then point to some research viewpoints that radically challenge the assumptions that underlie the assimilationist framework.