In this paper we present important correlations between immigration and labor market outcomes of native workers in the US. We use data on local labor markets, states and regions from the Census and American Community Survey over the period 1970-2010. We first look at simple correlations and then we use regression analysis with an increasing number of controls for observed and unobserved factors. We review the potential methods to separate the part of this correlation that captures the causal link from immigrants to native labor outcomes and we show estimates obtained with 2SLS method using the popular shift-share instrument. One fact emerging from all the specifications is that the net growth of immigrant labor has a zero to positive correlation with changes in native wages and native employment, in aggregate and by skill group. We briefly review the literature on the channels and the mechanisms that allow local economies to absorb immigrants with no negative (and possibly positive) impact on the labor demand for natives.