<p>how do you handle them?</p>

In domain names, you can do use IDN domains, if they are supported by the registrars you want to register them with.
Elsewhere in the URL, they are generally sent by the browser as utf8 urlencoded. Only recently I was looking at:
http://en.wikipedia.org/wiki/Pfeffern%C3%BCsse
And found it curious that there was a ü in the URL. Firefox shows it as a proper character though.