While most countries welcome (and some even subsidize) 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 can affect the productivity and wages of domestic firms. Using matched worker–firm data from Denmark and a matching difference‐in‐differences approach, we then find that firms that hire foreign experts instead of domestic experts become more productive, in the sense that they pay higher wages to high‐skilled co‐workers.