For longer elements

        <Router>
        <div>
            <Navbar totalItems={cart.total_items}/>
            <Routes>
                <Route exact path='/'>
                    <Route exact path='/' element={<Products products={products} onAddToCart={handleAddToCart}/>}/>
                </Route>
                <Route exact path='/cart'>
                    <Route exact path='/cart' element={<Cart cart={cart}/>}/>     
                </Route>
            </Routes>
        </div>
    </Router>

import { BrowserRouter as Router, Routes, Route, Link } from "react-router-dom";

function App() {
  return (
      <Router>
          <Routes>
            <Route path="/" element={<h1>home page</h1>} />
            <Route path="/seacrch" element={<h1>seacrch page</h1>} />
          </Routes>
      </Router>
  );
}

export default App;

Header will stay on all page

import React from 'react';

import {
  BrowserRouter,
  Routes,
  Route
} from "react-router-dom";

const Header = () => <h2>Header</h2>
const Dashboard = () => <h2>Dashboard</h2>
const SurveyNew = () => <h2>SurveyNew</h2>
const Landing = () => <h2>Landing</h2>


const App = () =>{
  return (
    <div>
      <BrowserRouter>
        <Header />
        <Routes >
        <Route exact path="/" element={<Landing />} />
        <Route path="/surveys" element={<Dashboard />}  />
        <Route path="/surveys/new" element={<SurveyNew/>}  />
        </Routes>
      </BrowserRouter>
    </div>
  );
};
export default App;

I ran into the same issue today and came up with the following solution based on this very helpful article by Andrew Luca

In PrivateRoute.js:

import React from 'react';
import { Navigate, Outlet } from 'react-router-dom';

const PrivateRoute = () => {
    const auth = null; // determine if authorized, from context or however you're doing it

    // If authorized, return an outlet that will render child elements
    // If not, return element that will navigate to login page
    return auth ? <Outlet /> : <Navigate to="/login" />;
}

In App.js (I've left in some other pages as examples):

import './App.css';
import React, {Fragment} from 'react';
import {BrowserRouter as Router, Route, Routes} from 'react-router-dom';
import Navbar from './components/layout/Navbar';
import Home from './components/pages/Home';
import Register from './components/auth/Register'
import Login from './components/auth/Login';
import PrivateRoute from './components/routing/PrivateRoute';

const App = () => {
  return (
    <Router>
      <Fragment>
        <Navbar/>
        <Routes>
          <Route exact path='/' element={<PrivateRoute/>}>
            <Route exact path='/' element={<Home/>}/>
          </Route>
          <Route exact path='/register' element={<Register/>}/>
          <Route exact path='/login' element={<Login/>}/>
        </Routes>
      </Fragment>
    </Router>
    
  );
}

In the above routing, this is the private route:

<Route exact path='/' element={<PrivateRoute/>}>
      <Route exact path='/' element={<Home/>}/>
</Route>

If authorization is successful, the element will show. Otherwise, it will navigate to the login page.

Only Route components can be a child of Routes. If you follow the v6 docs then you'll see the authentication pattern is to use a wrapper component to handle the authentication check and redirect.

function RequireAuth({ children }: { children: JSX.Element }) {
  let auth = useAuth();
  let location = useLocation();

  if (!auth.user) {
    // Redirect them to the /login page, but save the current location they were
    // trying to go to when they were redirected. This allows us to send them
    // along to that page after they login, which is a nicer user experience
    // than dropping them off on the home page.
    return <Navigate to="/login" state={{ from: location }} />;
  }

  return children;
}

...

<Route
  path="/protected"
  element={
    <RequireAuth>
      <ProtectedPage />
    </RequireAuth>
  }
/>

The old v5 pattern of create custom Route components no longer works. An updated v6 pattern using your code/logic could look as follows:

const PrivateRoute = ({ children }) => {
  const authed = isauth() // isauth() returns true or false based on localStorage
  
  return authed ? children : <Navigate to="/Home" />;
}

And to use

<Route
  path="/dashboard"
  element={
    <PrivateRoute>
      <Dashboard />
    </PrivateRoute>
  }
/>

Just set your router component to element prop:

<Routes>
  <Route exact path="/" element={<Home />} />
  <Route path="/about" element={<About />} />
  <Route path="/dashboard" element={<Dashboard />} />
</Routes>

You can also check for upgrading from v5, https://reactrouter.com/docs/en/v6/upgrading/v5

I know that this is not exactly the recipe how to make PirvateRoute work, but just wanted to mention that new docs recommend a slightly different approach to handle this pattern with react-router v6:

    <Route path="/protected" element={<RequireAuth><ProtectedPage /></RequireAuth>} />

import { Navigate, useLocation } from "react-router";

export const RequireAuth: React.FC<{ children: JSX.Element }> = ({ children }) => {
  let auth = useAuth();
  let location = useLocation();

  if (!auth.user) {
    return <Navigate to="/login" state={{ from: location }} />;
  }

  return children;
};

and you are supposed to add more routes inside ProtectedPage itself if you need it.

See docs and example for more details. Also, check this note by Michael Jackson that goes into some implementation details.

React Router v6, some syntactic sugar:

{auth && (
  privateRoutes.map(route =>
    <Route
      path={route.path}
      key={route.path}
      element={auth.isAuthenticated ? <route.component /> : <Navigate to={ROUTE_WELCOME_PAGE} replace />}
    />
  )
)}

for the Error "[Navigate] is not a component. All component children of must be a or <React.Fragment>"

use the following method maybe solved:

DefaultPage is when no match router, jump to the DefaultPage here use the <Route index element={} /> to replace the

<Navigate to={window.location.pathname + '/kanban'}/>

here is the link: https://reactrouter.com/docs/en/v6/getting-started/tutorial#index-routes

}/> }/> {/**/} } />

If you are using a second file to work on your index.js . Here is a more simple code snippet that may help others understand better. It is pretty straight forward and you do not require "exact" and "switch" to change between the paths thanks to the new version.

index.js

import React from "react";
import ReactDOM from "react-dom";

import { BrowserRouter } from "react-router-dom";

import "./index.css";
import App from "./App";

ReactDOM.render(
  <BrowserRouter>
    <App />
  </BrowserRouter>,
  document.getElementById("root")
);

App.js

Note that you need to import { Routes, Route } instead of { Route } (as it was in previous versions). Also, note that on the App.js file, it is not necessary to import BrowserRouter again.

import { Routes, Route } from "react-router-dom";

import AllPages from "./pages/AllPages";
import NewContactsPage from "./pages/ContactsPage";
import FavoritesPage from "./pages/Favorites";

function App() {

  return (
    <div>
      <Routes>
        <Route path="/" element={<AllPages />} />
        <Route path="/new-contacts" element={<NewContactsPage />} />
        <Route path="/favorites" element={<FavoritesPage />} />
      </Routes>
    </div>
  );
}

export default App;

Complement to reduce lines of code, make it more readable and beautiful.

This could just be a comment but I don't have enough points, so I'll put it as an answer.

Dallin's answer works but Drew's answer is better! And just to complete Drew's answer on aesthetics, I recommend creating a private component that takes components as props instead of children.

Very basic example of private routes file/component:

import { Navigate } from 'react-router-dom';

const Private = (Component) => {
    const auth = false; //your logic

    return auth ? <Component /> : <Navigate to="/login" />
}

Route file example:

<Routes>
    <Route path="/home" element={<Home />} />
    <Route path="/user" element={<Private Component={User} />} />
</Routes>