We investigate the effects of U.S. immigration in a comprehensive search and matching framework that allows for skill heterogeneity, imperfect substitutability between skilled and unskilled inputs, different search cost between natives and immigrants, cross‐skill matching, and imperfect transferability of foreign human capital. When we simulate the effects of the U.S. immigration that took place between the years 2000 and 2009, we find that both skilled and unskilled natives, as well as skilled and unskilled immigrants, gain in terms of income and employment. We also investigate the effects of an improvement in the transferability of human capital across borders and find that, although it has some redistributive effects, overall it benefits both immigrants and natives. (JEL F22, J61, J64)