We study the cultural integration of immigrants, estimating a structural model of marital matching along ethnic dimensions, exploring in detail the role of fertility, and possibly divorce in the integration process. We exploit rich administrative demographic data on the universe of marriages formed in Italy, as well as birth and separation records from 1995 to 2012. We estimate strong preferences of ethnic minorities' towards socialization of children to their own identity, identifying marital selection and fertility choices as fundamental socialization mechanisms. The estimated cultural intolerance of Italians towards immigrant minorities is also substantial. Turning to long-run simulations, we nd that cultural intolerances, as well as fertility and homogamy rates, slow-down the cultural integration of some immigrant ethnic minorities, especially Latin America, East Asia and Sub-Saharan Africa. Nonetheless, 75% of immigrants integrate into the majoritarian culture over the period of a generation. Interestingly, we show by counterfactual analysis that a lower cultural intolerance of Italians towards minorities would lead to slower cultural integration by allowing immigrants a more widespread use of their own language rather than Italian in heterogamous marriages. Finally, we quantitatively assess the effects of large future immigration inflows.