The title says it pretty well... How does Laravel implement clean URL and redirect them to the right Controllers.
Some frameworks like CakePHP use .htaccess to redirect everything to a FrontController which then dispatch the requests but laravel doesn't use .htaccess so i am bit confused.
Laravel use the concept of "routing", where all clean url are usually defined and mapped to something that will resolve to a view, such as controller action, anonymous functions, plain string, etc...
Each request will be caught by a file located at: public/index.php (that is done by a .htaccess file located at the same location). That index.php file will boostrap or illuminate the Laravel framework, and Laravel will run your code. How is it done? Routing.
The routing configuration is stored in a file located at app/routes.php where a route might look as follows:
Route::get('/users', 'UserController@showUsers');
Route::get('/users/create', 'UserController@createUser');
Route::post('/users/create', 'UserController@processCreateUser');
Route::get('/users/edit/{id}', 'UserController@createUser');
Route::post('/users/edit/{id}', 'UserController@processCreateUser');
More information about routing can be read at the documentation. I strongly recommend you to read the docs since routing are quite powerful in Laravel.
Laravel sites use the public/ folder as their document root. You'll find the .htaccess file in there.
public/ in Apache.
public directory as your document root via your web server.
.htaccessfile, see the source.