Interest in social and economic networks of various types has grown dramatically in the last two decades. The manifold empirical studies emphasize that networks often share two properties. First, they are small worlds – sparse networks with both short distances between pairs of agents, and strong local clustering. Second, they have skewed link distributions, often with a fat right tail. These properties have been observed in a wide variety of networks. A challenge in the economic, mostly game theoretic literature on network formation has been to capture these properties in a sound model. What incentives do (a few) agents have to form shortcuts, and why should they cluster locally? Why do a few agents acquire many links whereas many others seem able to form only a few ?