While most countries welcome (and some even subsidise) high-skilled immigrants, there is very limited evidence of their importance for domestic firms. To guide our empirical analysis, we first set up a simple theoretical model to show how foreign experts may impact on the productivity and wages of domestic firms. Using matched worker-firm data from Denmark and a difference-indifferences matching approach, we then find that firms that hire foreign experts – defined as employees eligible for reduced taxation under the Danish "Tax scheme for foreign researchers and key employees" – both become more productive (pay higher wages) and increase their exports of goods and services.