I will present an overview of recent work on network games. Agents interact with their neighbors in a fixed network and choose their actions according to linear best-replies. These games have been applied to the study of criminal activity, public goods, Cournot competition and also underlie econometric models of peer effects. The objective is to understand how Nash equilibria depend on the structure of the network. In particular : How does the position of an agent in the network affect his action ? How do the properties of the equilibria - uniqueness, multiplicity, interiority - depend on the shape of the network ? How do equilibria change when the network expands ? I will present recent results on these questions involving the notions of Bonacich centrality, lowest eigenvalue, and broken interdependence.