We examine both theoretically and empirically how migration affects cultural change in home and host countries. Our theoretical model integrates various compositional and cultural transmission mechanisms of migration-based cultural change for which it delivers distinctive testable predictions on the sign and direction of convergence. We then use the World Value Survey for the period 1981-2014 to build time-varying measures of cultural similarity for a large number of country pairs and exploit within country-pair variation over time. Our evidence is inconsistent with the view that immigrants are a threat to the host country’s culture. While migrants do act as vectors of cultural diffusion and bring about cultural convergence, this is mostly to disseminate cultural values and norms from host to home countries (i.e., cultural remittances).