Routing topologies for distributed hashing in peer-to-peer networks are classified into two categories: deterministic and randomized. A general technique for constructing deterministic routing topologies is presented. Using this technique, classical parallel interconnection networks can be adapted to handle the dynamic nature of participants in peer-to-peer networks. A unified picture of randomized routing topologies is also presented. Two new protocols are described which improve average latency as a function of out-degree. One of the protocols can be shown to be optimal with high probability. Finally, routing networks for distributed hashing are revisited from a systems perspective and several open design problems are listed.