In this thesis, I propose two models on opinion formation in social networks that account for confirmation bias and persistent disagreement and one model of conflict that explicitly models alliances and enmities in a network framework to study the Sudan conflict. In the first chapter, titled "Confirmation Bias in Social Networks", I propose a social learning model that investigates how confirmatory bias affects public opinion when agents exchange information over a social network. For that, besides exchanging opinions with friends, individuals observe a public sequence of potentially ambiguous signals and they interpret it according to a rule that accounts for confirmation bias. I first show that, regardless the level of ambiguity and both in the case of a single individual or of a networked society, only two types of opinions might be formed and both are biased. One opinion type, however, is necessarily less biased (more efficient) than the other depending on the state of the world. The size of both biases depends on the ambiguity level and the relative magnitude of the state and confirmatory biases. In this context, long-run learning is not attained even when individuals interpret ambiguity impartially. Finally, since it is not trivial to ascertain analytically the probability of emergence of the efficient consensus when individuals are connected through a social network and have different priors, I use simulations to analyze its determinants. Three main results derived from this exercise are that, in expected terms, i) some network topologies are more conducive to consensus efficiency, ii) some degree of partisanship enhances consensus efficiency even under confirmatory bias and iii) open-mindedness, i.e. when partisans agree to exchange opinions with other partisans with polar opposite beliefs, might harm efficiency in some cases. In the second chapter, titled "Social Media Networks, Fake News and Polarization" (joint with M. Azzimonti), I study how the structure of social media networks and the presence of fake news might affect the degree of misinformation and polarization in a society. To that end, we construct a set of heterogeneous random graphs and simulate the information exchange process over a long horizon to quantify the bots' ability to spread fake news. A key insight is that significant misinformation and polarization arise in networks in which only 10% of agents believe fake news to be true, indicating that network externality effects are quantitatively important. In the third chapter, titled "Sudan Conflict: A Network Approach" (joint with C. Rubbini and A. Ponce), I apply a theory of conflict that explicitly models alliances and enmities in a network framework to study the Sudan conflict. We build a panel dataset at the fighting group, covering the period 2003-2010, using ACLED data and estimate the networks externalities of armed groups. A key player analysis is ongoing but suggests how to optimally intervene in a way that the death toll of the conflict might be reduced.