Arriving is the start of a migrant's story, not the end. What happens over the following years and generations decides whether newcomers become full members of a society or remain outsiders, and both migrants and the receiving society shape that outcome.

Melting pot and mosaic

The playwright Israel Zangwill gave one ideal its name in his 1908 play The Melting Pot, in which a young immigrant declares: "America is God's Crucible, the great Melting-Pot where all the races of Europe are melting and re-forming!" Assimilation imagines immigrants blending into one new shared people, adopting the language and customs of the majority over time. Its defenders argue that a shared language and common norms open doors to equal opportunity and hold a diverse society together. Its critics point to the history of forced assimilation, in which children were punished for speaking their parents' language, and argue that it asks only the newcomer to change.

Multiculturalism offers a different picture: a mosaic in which groups keep distinct identities within a common political framework. Canada became the first country to adopt multiculturalism as official policy in 1971. Defenders see recognition of minority cultures as a matter of dignity and freedom. Critics argue that it can harden group boundaries, and the political theorist Susan Moller Okin argued that group rights can shield practices that harm women within those groups. In 2010 and 2011 the leaders of Germany and Britain both declared that multiculturalism had failed in their countries, though scholars dispute whether those countries had ever practised it as fully as the speeches implied.

Since the late 1990s many European states have adopted a third approach, civic integration. Civic integration policies require newcomers to take language and civics courses or tests, sometimes before they may even arrive, as the Netherlands began requiring in 2006. Supporters say this gives migrants the tools to succeed; critics say it can become a barrier aimed at keeping certain groups out.

What actually happens

Research on outcomes shows a few strong patterns. One concerns language. Immigrants often keep their first language, their children grow up bilingual, and their grandchildren usually speak only the host language. This three-generation pattern has held across many groups and countries, though large, continuous communities can slow it.

Another finding is that integration does not follow one path. In 1993 the sociologists Alejandro Portes and Min Zhou proposed segmented assimilation: the children of immigrants may follow different paths. Some rise into the middle class, some join the poorest parts of society and stay there, and some advance economically while keeping close ties to their parents' community. Which path a child follows depends on family resources, the reception the group receives and the neighbourhood they grow up in.

Public beliefs often lag behind reality. In surveys across several rich countries, economists Alberto Alesina, Armando Miano and Stefanie Stantcheva found that people greatly overestimate the share of immigrants in their country, often guessing two or three times the true figure, and also overestimate their dependence on welfare.

Becoming a citizen

Countries grant citizenship at birth in two main ways. Jus soli, the right of the soil, grants citizenship by place of birth; it is the norm across the Americas. The Fourteenth Amendment of 1868 declares that "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States." Jus sanguinis, the right of blood, grants citizenship through a parent, and long dominated in Europe and Asia. Adults can usually naturalise after years of residence, often with tests of language and civics and an oath.

Where naturalisation is hard, a large class of denizens, long-term residents who lack citizenship and the vote, can build up. They pay taxes and obey laws they have no part in making, which raises a question for democracy: who counts as the people?

Attitudes to dual citizenship have shifted too. Many countries once required new citizens to give up their old nationality; today most accept dual citizenship in some form, on the view that a person can be loyal to a new home without denying the old one.

Worked example: three generations in Germany

Mehmet came to West Germany from Anatolia in 1969 as a guest worker. He learned enough German for the factory, but his social life stayed in Turkish. His daughter Ayşe was born in Cologne in 1975. She grew up bilingual and went to German schools, yet under German law she was a Turkish citizen, a foreigner in the only country she knew. Germany's 2000 reform granted citizenship at birth to children born there if a parent had lived in Germany lawfully for years, though such children long had to choose between passports as young adults. Ayşe's son, born in 2003, became German at birth. He speaks Turkish haltingly with his grandfather and German everywhere else. The family's story follows the three-generation language pattern, shows how a shift toward jus soli changes membership, and shows segmented assimilation at work: the outcome depended on schooling, law and welcome, not on the family alone.