So how does React know which parts of the model need reconciling, without traversing the complete model and/or the complete state on every update?
The React API will also let a component decide for itself if it should be rendered.
State in React is local to a component, but it can be passed down to a component's children in the form of props.
Centralized state can be achieved using a library like Redux, where an individual component subscribes to an external data store's changes. Redux abstracts the details away, but under the hood it's still just setState.