"Assimilation," a protean concept with an American pedigree and a checkered past, is back in vogue. But in academic and colloquial usage, in social science, public policy and popular culture, the idea and the ideal of “assimilation” have had a bumpy history. Over time the term has conflated various normative prescriptions (“e pluribus unum,” “melting pot”) and empirical descriptions (cultural adaptations, economic mobility, social acceptance by a dominant group) to make sense of the incorporation of “ethnic” difference in American life. After more than a century of use and misuse the term itself remains confusing and contentious. For a “canonical” concept, there remains surprising ambiguity as to its meaning, measurement and applicability. This essay, prepared for a Festschrift in honor of Herbert J. Gans, explores the history of the idea in American society and social science as a master frame and the teleology of Progress underlying it; considers cultural, social, legal, economic and identificational indices of intergenerational change among contemporary ethnic groups based on an array of census and survey data; and raises questions about the limitations and paradoxes of the concept itself in the study of ethnicity and inequality in American life. Despite the grand narratives of modernization which undergird the concept of assimilation, neither race nor religion nor ethnicity has vanished in American life. Linguistic “Anglicization” and other forms of acculturation do proceed rapidly, especially among immigrant children and the second generation. But alongside undeniable upward social mobility from the first to the second generation for most groups, especially the children of the poorest and least educated - though the gains appear to peak in the second generation and decline or plateau thereafter - there is compelling evidence of widening “ethclass” and legal inequalities, of new conflicts and political mobilizations around ethnic and racial issues, and of downward mobility and marginalization for vulnerable segments of these populations. An undocumented status has become a caste-like master status blocking access to the opportunity structure and paths to social mobility for millions of immigrants. A fraught concept like “assimilation,” weighted by the normative baggage of its past, seems ill-suited to grasp these complex dynamics and to focus critical attention on enduring structural inequalities and persistent ethnic and pan-ethnic formations in this “permanently unfinished” society.