We move the actual server request and response logic out of the component, of course, so it's just a one-liner within that component.
Instagram got really far with that, but there are parts of Instagram (converted from an earlier Backbone version) that have the child components directly update Backbone models which then handle the server requests. The on change Backbone events then trigger setState() calls on our UI.
At Facebook we have an in-house dataflow architecture that updates our components.
So it really depends on how you want to do it. But we don't provide a "React.Data" or "React.Router" or anything like that. This is by design, since we can't possibly account for everyone's specific use case.