We present a novel theory of belief dynamics that explains the interplay between internal beliefs in people’s minds and beliefs of others in their external social environments. The Networks of Belief theory goes beyond existing theories of belief dynamics in three ways. First, it provides an explicit connection between belief networks in individual minds and belief dynamics on social networks. The connection, absent from previous theories, is established through people’s social beliefs, or perceived beliefs of others. Second, the theory recognizes that the correspondence between social beliefs and others’ actual beliefs can be imperfect, because social beliefs are affected by personal beliefs as well as by the actual beliefs of others. Past theories of belief dynamics on social networks do not distinguish between perceived and actual beliefs of others. Third, the theory explains diverse belief dynamics phenomena parsimoniously through the differences in attention and the resulting felt dissonances in personal, social, and external parts of belief networks. We implement our theoretical assumptions in a computational model within a statistical physics framework and derive novel model predictions. We find support for our theoretical assumptions and model predictions in two large survey studies (N1=973, N2=669). We then derive novel insights about diverse phenomena related to belief dynamics, including group consensus and polarization, group radicalization, minority influence, and different empirically observed belief distributions. We discuss how the theory goes beyond different existing models of belief dynamics and outline promising directions for future research.