Configuration changes are a common source of instability in networks, leading to outages, performance disruptions, and security vulnerabilities. Even when the initial and final configurations are correct, the update process itself often steps through intermediate configurations that exhibit incorrect behaviors. This paper introduces the notion of consistent network updates - updates that are guaranteed to preserve well-defined behaviors when transitioning mbetween configurations. We identify two distinct consistency levels, per-packet and per-flow, and we present general mechanisms for implementing them in Software-Defined Networks using switch APIs like OpenFlow. We develop a formal model of OpenFlow networks, and prove that consistent updates preserve a large class of properties. We describe our prototype implementation, including several optimizations that reduce the overhead required to perform consistent updates. We present a verification tool that leverages consistent updates to significantly reduce the complexity of checking the correctness of network control software. Finally, we describe the results of some simple experiments demonstrating the effectiveness of these optimizations on example applications.