The combination of two inexorable trends---increasing parallelism and increasing big data analytics---means modern data centers urgently need efficient high-capacity networks interconnecting thousands of servers. But we have lacked a fundamental understanding of what network topologies achieve high throughput. This talk shows how surprisingly, today's carefully-structured designs such as fat-trees are far from optimal. Our Jellyfish architecture uses a completely random network to achieve substantially higher throughput than deployed designs, and allows easy incremental expansion. This leads to numerous important theoretical and practical questions in network design, such as optimality and the design of heterogeneous networks.