React encourages you to use a parent component that controls the state and passes it down to it's children via props.

Passing data to separate components without a shared parent is outside of what React is trying to accomplish but I've handled it before by passing a Backbone model to the separate components as props.

If you're passing it to child components you pass it through attributes. If you're passing up to parents, however, you have to create a function on the parent that will get called to accept the child's new data. This can get really messy if you have deeply nested components and need to get data from one branch to another branch.

I have been successful by instantiating separate services to perform REST operations and a global event emitter to establish communication between all the services and all the components that relate to these services in any way.