Social networks form the basic medium of social interaction. The structure of these networks significantly impacts and co-evolves with the behavioral patterns of society. Important societal outcomes – the global reach of an epidemic, the degree of cooperation in an online network, the adoption of new technologies – are dictated by social networks.In this talk, we explore the impact of networks on segregation. In 1969, economist Thomas Schelling introduced a landmark model of racial segregation in which individuals move out of neighborhoods where their ethnicity constitutes a minority. Simple simulations of Schelling's model suggest that this local behavior can cause global segregation effects. In this talk, we provide a rigorous analysis of Schelling's model on ring networks. Our results show that, in contrast to prior interpretations, the outcome is nearly integrated: the average size of an ethnically-homogenous region is independent of the size of the society and only polynomial in the size of a neighborhood.Joint work with Christina Brandt, Gautam Kamath, and Robert D. Kleinberg.