React Router 4 is fundamentally different because it allows for nested routes that rely on parent context. This facilitates recursive routes and other B-E-A-UTIFUL things.

NestedRoutes.js

import React from 'react'
import {
  BrowserRouter as Router,
  Route,
  Link
} from 'react-router-dom'

const BasicExample = () => (
  <Router>
    <div>
      <ul>
        <li><Link to="/topics">Topics</Link></li>
      </ul>
      <Route path="/topics" component={Topics}/>
    </div>
  </Router>
)

const Topics = ({ match }) => (
  <div>
    <h2>Topics</h2>
    <ul>
      <li><Link to={`${match.url}/rendering`}>Rendering with React</Link></li>
      <li><Link to={`${match.url}/components`}>Components</Link></li>
      <li><Link to={`${match.url}/props-v-state`}>Props v. State</Link></li>
    </ul>

    <Route path={`${match.url}/:topicId`} component={Topic}/>
    <Route exact path={match.url} render={() => (
      <h3>Please select a topic.</h3>
    )}/>
  </div>
)

const Topic = ({ match }) => (
  <div>
    <h3>{match.params.topicId}</h3>
  </div>
)

export default BasicExample