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Serverless computing is an emerging paradigm in which an application's resource provisioning and scaling are managed by third-party services. Examples include AWS Lambda, Azure Functions, and Google Cloud Functions. Behind these services' easy-to-use APIs are opaque, complex infrastructure and management ecosystems. Taking on the viewpoint of a serverless customer, we conduct the largest measurement study to date, launching more than 50,000 function instances across these three services, in order to characterize their architectures, performance, and resource management efficiency. We explain how the platforms isolate the functions of different accounts, using either virtual machines or containers, which has important security implications. We characterize performance in terms of scalability, coldstart latency, and resource efficiency, with highlights including that AWS Lambda adopts a bin-packing-like strategy to maximize VM memory utilization, that severe contention between functions can arise in AWS and Azure, and that Google had bugs that allow customers to use resources for free.