European/UNESCO interculturalism (IC) emerged as a critique of multiculturalism (MC) (complicated by the fact that there is an alternative interculturalism, not discussed here). I suggest that this relationship has gone through three phases. "Phase one" begins in the 1990s with a general dissatisfaction with MC from many political and intellectual sources. "Phase two," roughly from about the middle of the last decade, is when IC scholars, mainly sociologists, though also in cultural studies, policy studies, migration studies, geography as well as education emerge in significant numbers. The engagement with multiculturalism is limited and serves the purpose of clearing the ground in order to get on with a new research approach and then getting on with it. "Phase three" is the political theory justification of IC. I argue that these three phases have not established a pro-diversity 'ism' which can replace MC. While I hope we may move on to a "phase four," where MC and IC are seen to be complementary, I here re-state what I think are the key concepts of MC. I hope it will be evident that firstly, that these concepts are not out of date or redundant; and secondly, therefore, that IC is wrong to abandon them.