Fluency in (or ease to quickly learn) the language of the destination country plays a key role in the transfer of human capital from the source country to another country and boosts the immigrant's rate of success at the destination's labor market. This suggests that the ability to learn and speak a foreign language might be an important factor in the migration decision. We use a novel dataset on immigration flows and stocks of foreigners in 30 OECD destination countries from 223 source countries for the years 1980-2009 and a wide range of linguistic indicators to study the role of language in shaping international migration. Specifically, we investigate how both linguistic distance and linguistic diversity, as a proxy for the "potential" ease to learn a new language and to adapt to a new context, affect migration. We find that migration rates increase with linguistic proximity and the result is robust to the inclusion of genetic distance as a proxy for cultural proximity and to the use of multiple measures of linguistic distance. Interestingly, linguistic proximity matters more for migrants moving into non-English speaking destinations than to English-speaking countries. The likely higher proficiency of the average migrant in English rather than in other languages may diminish the relevance of the linguistic proximity indicators to English speaking destinations. Finally, destinations that are linguistically more diverse and polarized attract fewer migrants than those with a single language; whereas more linguistic polarization at origin seems to act as a push factor.