In the first part of this paper, we present a stylised model of the labour market impact of immigration. We then discuss mechanisms through which an economy can adjust to immigration: changes in factor prices, output mix and production technology. In the second part, we explain the problems of empirically estimating how immigration affects labour market outcomes of the resident population and review some strategies to address these. We then summarise some recent empirical studies for the UK and other countries. We conclude with an outlook of what we believe are important avenues for future research.