Updated solution for React router v4

<Route 
  path="/some-path" 
  render={() => !isAuthenticated ?
    <Login/> :
    <Redirect to="/some-path" />
}/>

React router up to v3

Use 'onEnter' event and in callback check if the user is authorized:

<Route path="/" component={App} onEnter={someAuthCheck}>  

const someAuthCheck = (nextState, transition) => { ... }

With react-router 4 you have access to the Route props inside the component. To redirect a user you just have to push the new URL to the history. In your example, the code would be:

var Dashboard = React.createClass({
  componentWillMount: function () {
    const history = this.props.history; // you'll have this available
    // You have your user information, probably from the state
    // We let the user in only if the role is 'admin'
    if (user.role !== 'admin') {
      history.push('/'); // redirects the user to '/'
    }
  },

  render: function () {
    return (
      <h1>Welcome</h1>
    );
  }
});

At the docs, they show another way to do it, by using the render property, instead of component. They define a PrivateRoute, that makes the code very explicit when you define all your routes.