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The increasing popularity of blockchain-based cryptocurrencies has made scalability a primary and urgent concern. We analyze how fundamental and circumstantial bottlenecks in Bitcoin limit the ability of its current peer-to-peer overlay network to support substantially higher throughputs and lower latencies. Our results suggest that reparameterization of block size and intervals should be viewed only as a first increment toward achieving next-generation, high-load blockchain protocols, and major advances will additionally require a basic rethinking of technical approaches. We offer a structured perspective on the design space for such approaches. Within this perspective, we enumerate and briefly discuss a number of recently proposed protocol ideas and offer several new ideas and open challenges.