Modern peer-to-peer networks consist of several network layers and distributed algorithms providing features like indexing, ressource balancing, entry protocols, security, anonymity, and cryptography. Since peer-to-peer networks are highly dynamic, a fundamental task in the design of these networks is to provide high connectivity. We propose a solution by distributed random link exchange algorithms such that the overlay network can be connected random graphs. Such random graphs are expander graphs with high probability which are robust against node and edge failures. Furthermore these random networks have low diameter and small degree. In this paper we survey recent work.