Structured peer-to-peer overlay networks have recently emerged as good candidate infrastructure for building novel large-scale and robust Internet applications in which participating peers share computing resources as equals. In the past three year, various structured peer-to-peer overlay networks have been proposed, and probably more are to come. We present a framework for understanding, analyzing and designing structured peer-to-peer overlay networks. The main objective of the paper is to provide practical guidelines for the design of structured overlay networks by identifying a fundamental element in the construction of overlay networks: the embedding of k-ary trees. Then, a number of effective techniques for maintaining these overlay networks are discussed. The proposed framework has been effective in the development of the DKS system.