There is public and scholarly debate about the effects of personalized recommender systems implemented in online social networks, online markets, and search engines. On the one hand, it has been warned that personalization algorithms generate homogenous information diets that tend to confirm previously held attitudes and beliefs. Opinionated social media posts, shared news items, and online discussion could fragment social groups, alienate users with different political views, and ultimately foster opinion polarization. On the other hand, critics of this “personalization-polarization hypothesis” argue that the effects of personalization algorithms on information diets are too weak to have meaningful effects. Here, we argue that contributions to both sides of the debate fail to consider the complexity that arises when large numbers of interdependent Internet users interact and exert influence on one another in algorithmically governed communication systems. Reviewing insights from the literature of opinion dynamics in social networks, we demonstrate that opinion dynamics can be critically influenced by mechanisms active on three levels of analysis: the individual, local, and global level. We show which theoretical and empirical research on these three levels is needed to answer the question whether personalization fosters polarization or not, advocating an approach that combines rigorous theoretical modeling with the emergent field of data science.