I had to write my own router, but the event system [1] allows you to catch left-clicks or touch events and let you decide how to handle them and the lifecycle functions [2] allow you to update history/URL params to reflect the state of your app. If you have app state which isn't easily serializeable, then you'd have difficulty providing a good URL structure for people but you'd probably have that issue even if you weren't using react.

1: https://facebook.github.io/react/docs/events.html

2: https://facebook.github.io/react/docs/component-specs.html