We find information through our social network. A network of banks handles our financial transactions. And when computers freeze under virus attacks, we are reminded of how pervasive networks are. This work concentrates on two topics. The first part of the thesis studies how highly unequal networks, where links are concentrated on a few key nodes, can emerge. The interest is motivated by how their structure affects their function: the spread of information and disease, for instance, may occur faster in such networks The second part of the thesis applies network theories to gain a better understanding of financial systems. We investigate the strategic motivations of banks to interact with each other when the banking system is exposed to the danger of contagion.