We present Statesman, a network-state management service that allows multiple network management applications to operate independently, while maintaining network-wide safety and performance invariants. Network state captures various aspects of the network such as which links are alive and how switches are forwarding traffic. Statesman uses three views of the network state. In observed state, it maintains an up-to-date view of the actual network state. Applications read this state and propose state changes based on their individual goals. Using a model of dependencies among state variables, Statesman merges these proposed states into a target state that is guaranteed to maintain the safety and performance invariants. It then updates the network to the target state. Statesman has been deployed in ten Microsoft Azure datacenters for several months, and three distinct applications have been built on it. We use the experience from this deployment to demonstrate how Statesman enables each application to meet its goals, while maintaining network-wide invariants.