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This article provides background information about interconnection networks, an analysis of previous developments, and an overview of the state of the art. The main contribution of this article is to highlight the importance of the interpolation and extrapolation of technological changes and physical constraints in order to predict the optimum future interconnection network. The technological changes are related to three of the most important attributes of interconnection networks: topology, routing, and flow-control algorithms. On the other hand, the physical constraints, that is, port counts, number of communication nodes, and communication speed, determine the realistic properties of the network. We present the state-of-the-art technology for the most commonly used interconnection networks and some background related to often-used network topologies. The interconnection networks of the best-performing petascale parallel computers from past and present Top500 lists are analyzed. The lessons learned from this analysis indicate that computer networks need better performance in future exascale computers. Such an approach leads to the conclusion that a high-radix topology with optical connections for longer links is set to become the optimum interconnect for a number of relevant application domains.