The standard empirical analysis of immigration, based on a simple labor demand and labor supply framework, has emphasized the negative impact of foreign born workers on the average wage of U.S.-born workers (particularly of those without a high school degree). A precise assessment of the average and relative effects of immigrants on U.S. wages, however, needs to consider labor as a differentiated input in production. Workers of different educational and experience levels are employed in different occupations and are therefore imperfectly substitutable. When taking this approach, one realizes that foreign-born workers are "complements" of U.S.-born workers in two ways. First, foreign-born residents are relatively abundant in the educational groups in which natives are scarce. Second, their choice of occupations for given education and experience attainments is quite different from that of natives. This implies that U.S.- and foreign-born workers with similar education and experience levels are imperfectly substitutable. Accounting carefully for these complementarities and for the adjustment of physical capital induced by immigration, the conventional finding of immigration’s impact on native wages is turned on its head: overall immigration over the 1980- 2000 period significantly increased the average wages of U.S.-born workers (by around 2%). Considering its distribution across workers, such an effect was positive for the wage of all native workers with at least a high school degree (88% of the labor force in year 2000), while it was null to moderately negative for the wages of natives without a high school degree.