This paper reviews the recent evidence on U.S. immigration, focusing on two key questions: (1) Does immigration reduce the labor market opportunities of less-skilled natives? (2) Have immigrants who arrived after the 1965 Immigration Reform Act successfully assimilated? Looking across major cities, differential immigrant inflows are strongly correlated with the relative supply of high school dropouts. Nevertheless, data from the 2000 Census shows that relative wages of native dropouts are uncorrelated with the relative supply of less-educated workers, as they were in earlier years. At the aggregate level, the wage gap between dropouts and high school graduates has remained nearly constant since 1980, despite supply pressure from immigration and the rise of other education-related wage gaps. Overall, evidence that immigrants have harmed the opportunities of less educated natives is scant.
That is from David Card, here is the paper. And there is more:
On the question of assimilation, the success of the U.S.-born children of immigrants is a key yardstick. By this metric, post-1965 immigrants are doing reasonably well: second generation sons and daughters have higher education and wages than the children of natives. Even children of the least educated immigrant origin groups have closed most of the education gap with the children of natives.