react-router vs react-router-dom, when to use one or the other?

Just use react-router-dom - react-router-dom re-exports all of react-router. The link on GitHub answer (what's the diff between react-router-dom & react-router?).

react-router-dom is a react-router plus:

• <BrowserRouter> which is <Router history={browserNativeHistoryApiWrapper}/>

  proof: https://github.com/ReactTraining/react-router/blob/master/packages/react-router-dom/modules/BrowserRouter.js

• some Link improvements for browser

  proof: https://github.com/ReactTraining/react-router/blob/master/packages/react-router-dom/modules/Link.js

• and with <NavLink> — wrapper that knows if it's "active" or not

  proof: https://github.com/ReactTraining/react-router/blob/master/packages/react-router-dom/modules/NavLink.js

react-router contains all the common components between react-router-dom and react-router-native. When should you use one over the other? If you're on the web then react-router-dom should have everything you need as it also exports the common components you'll need. If you're using React Native, react-router-native should have everything you need for the same reason. So you'll probably never have to import anything directly from react-router. As far as when you use

<Router history={browserHistory}>

vs

<Router>

In RRv4 you won't need to pass down browserHistory, that was just for previous versions of the router.

If you're still confused, you can check out the details on each package here