We present new operational semantics for serverless computing that model the event-driven relationships between serverless functions, as well as their interaction with platform services such as databases and object stores. These semantics precisely encapsulate how control transfers between functions, both directly and through reads and writes to platform services. We use these semantics to define the notion of the service call graph for serverless applications that captures program flows through functions and services. Finally, we construct service call graphs for 12 serverless JavaScript applications, using a prototype of our call graph construction algorithm, and we evaluate their accuracy.