In comparing different countries, studies often seek to account for the success of immigrant integration, or lack of it, in a small number of 'grand ideas,' such as nationally specific 'models' of integration, which attempt to provide overarching explanations for cross-national differences and similarities. This article evaluates five grand ideas in light of our study examining how four European (Britain, France, Germany, and the Netherlands) and two North American (U.S., Canada) countries are meeting the challenges of integrating immigrants and their second-generation children across a variety of domains from the labor market, to the educational system, to the polity. We conclude that while some of the grand ideas help to illuminate patterns of integration in particular domains, none provides a sufficiently encompassing explanation - and each has significant failings. Moreover, none of these ideas highlights all of the features that we argue are critical, although these do not boil down to one 'grand narrative.' These features are the characteristics or qualities that immigrants bring with them when they move to Europe or North America; demographic and other social and economic trends there; and, perhaps most important, historically rooted social, political, and economic institutions in each receiving society that create barriers as well as bridges to integration and inclusion. [ABSTRACT FROM AUTHOR]