redirection to index.php

Hi Folk

I would like to have "virtual" urls on my php site. Meaning, that
people (and search engines) can go to
www.mysite.com/myurl.php or
to www.mysite.com/mysubject/mytopic/

and that these requests get redirected to www.mysite.com/index.php,
while the user keeps seeing the original url in their header bar and
does not notice the redirection.

Meanwhile in index.php, the php works out where the user came from and
serves the appropiate page....

Can this be done?
Is it recommended?
How should I do it?
Do I need to create the actual folders?

Thanks a million

> Nicolaas