Music streaming platforms allow users to enjoy music from all over the globe.Such opportunity speeds up cultural exchange between different countries, a process often associated with globalization. While such an exchange could lead to more diverse music consumption, empirical evidence on its influence on online music consumption is limited. Besides, the extent to which music recommender systems foster exchange or amplify globalization in music remains an understudied problem.In this paper, we present findings from an empirical study to detect traces of globalization in domestic vs. foreign online music consumption. Besides, we investigate if popular recommendation algorithms, specifically ItemKNN and NeuMF, are prone to amplifying globalization processes. Our experiments on Last.fm listening data show nuanced patterns of globalization in music consumption. We observe a strong position of US music in all considered countries. In countries such as Sweden, Great Britain, or Brazil, US music shows various levels of coexistence with domestic music. We find that Finland is least influenced by US music, while greatly consuming and 'exporting' domestic music. With respect to recommendation algorithms, ItemKNN tends to recommend domestic music to users of many countries, while NeuMF contributes to accelerating globalization and shifting balance towards dominance of US music on the market.