Considering you are using react-router v4

Use your component with withRouter and use history.push from props to change the route. You need to make use of withRouter only when your component is not receiving the Router props, this may happen in cases when your component is a nested child of a component rendered by the Router and you haven't passed the Router props to it or when the component is not linked to the Router at all and is rendered as a separate component from the Routes.

import {withRouter} from 'react-router';

class App extends React.Component {
     ...
     componenDidMount() {
        // get isLoggedIn from localStorage or API call
        if (isLoggedIn) {
             // dispatch an action to change the route
             this.props.history.push('/home');
        }
     }
     render() {
         // return login component
         return <Login />
    }
}


export default withRouter(App);

Important Note

If you are using withRouter to prevent updates from being blocked by shouldComponentUpdate, it is important that withRouter wraps the component that implements shouldComponentUpdate. For example, when using Redux:

// This gets around shouldComponentUpdate

withRouter(connect(...)(MyComponent))

// This does not

connect(...)(withRouter(MyComponent))

or you could use Redirect

import {withRouter} from 'react-router';

class App extends React.Component {
     ...
     render() {
         if(isLoggedIn) {
              return <Redirect to="/home"/>
         }
         // return login component
         return <Login />
    }
}

With react-router v2 or react-router v3, you can make use of context to dynamically change the route like

class App extends React.Component {
     ...
     render() {
         if (isLoggedIn) {
             // dispatch an action to change the route
             this.context.router.push('/home');
         }
         // return login component
         return <Login />
    }
}

App.contextTypes = {
    router: React.PropTypes.object.isRequired
}
export default App;

or use

import { browserHistory } from 'react-router';
browserHistory.push('/some/path');

In react-router version 4:

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

const Example = () => (

  if (isLoggedIn) {
    <OtherComponent />

  } else {

    <Router>
      <Redirect push to="/login" />
      <Route path="/login" component={Login}/>
    </Router>

  }
)

const Login = () => (
    <h1>Form Components</h1>
    ...
)

export default Example;

Another alternative is to handle this using Thunk-style asynchronous actions (which are safe/allowed to have side-effects).

If you use Thunk, you can inject the same history object into both your <Router> component and Thunk actions using thunk.withExtraArgument, like this:

import React from 'react'
import { BrowserRouter as Router, Route, Redirect} from 'react-router-dom'
import { createBrowserHistory } from "history"
import { applyMiddleware, createStore } from "redux"
import thunk from "redux-thunk"

const history = createBrowserHistory()

const middlewares = applyMiddleware(thunk.withExtraArgument({history}))
const store = createStore(appReducer, middlewares)

render(
  <Provider store={store}
    <Router history={history}>
      <Route path="*" component={CatchAll} />
    </Router
  </Provider>,
appDiv)

Then in your action-creators, you will have a history instance that is safe to use with ReactRouter, so you can just trigger a regular Redux event if you're not logged in:

// meanwhile... in action-creators.js
export const notLoggedIn = () => {
  return (dispatch, getState, {history}) => {
    history.push(`/login`)
  }
}

Another advantage of this is that the url is easier to handle, now, so we can put redirect info on the query string, etc.

You can try still doing this check in your Render methods, but if it causes problems, you might consider doing it in componentDidMount, or elsewhere in the lifecycle (although also I understand the desire to stick with Stateless Functional Compeonents!)

You can still use Redux and mapDispatchToProps to inject the action creator into your comptonent, so your component is still only loosely connected to Redux.