Technically speaking you would need one single rule in your web server configuration that rewrites all urls to a single router.php file (for instance), and code

Technically speaking you would need one single rule in your web server configuration that rewrites all urls to a single router.php file (for instance), and code there your own logic to handle urls in PHP. This is not very different from other server languages except for the fact that you are in control of the routing logic AND you can delegate it to a framework if you choose to do so. I've been using this technique (single url rewrite rule, send everything to index.php, handle routing there) for some time and it's worked quite well for me.