When you edit a question on stackoverflow.com, you will be redirected to a URL like this:
https://stackoverflow.com/posts/1807421/edit
Using mod_rewrite this can be achieved very easily.
With apache and PHP, you might perform one of your examples using a mod_rewrite rule in your apache config as follows:
RewriteEngine On
RewriteRule ^/posts/(\d+)/edit /posts/edit.php?id=$1
This looks for URLs of the "clean" form, and then rewrites them so that they are internally redirected to a particular PHP script.
Quite often rules like this are used to route all requests into a common controller script, which might do something like instantiate a "PostsController" class and ask it to handle an edit request. This is a common feature of most PHP application frameworks.