Domain names are currently ASCII-only. Which means unless your language is American English you probably can't have a web site with a name that's written properly. There's a long standing effort to create International Domain Names, led by the IETF IDN working group. Now it's about to become a reality with ICANN's endorsement.
The technology problem is fascinating. The right solution is to fix DNS to use UTF-8. But no one thinks we can update the zillions of programs that assume DNS is ASCII. So the recommendation is to encode Unicode in ASCII via Punycode. Slap xn-- in front of the encoded name and poof you have an IDN. crèmebrûlée.com becomes xn--crmebrle-20ap0r.com. Try yourself!
How are users going to see these names? The plan is to augment web browsers, email clients, etc. with software to handle Punycode. Internet Explorer is already halfway there, thanks to Microsoft's interception of broken URLs. Verisign released a preliminary browser helper that augments IE for IDNs (with a now-obsolete encoding). Expect many more to follow. I'm not convinced it will work.
The political problem is also fascinating. Domain registrars stand to make a fortune registering new names. They're impatient. Verisign has been selling IDNs for a year with the now-obsolete RACE encoding; there's a debate whether to grandfather them in. Verisign even threatened to violate the DNS standard. And a lot of people still disagree with the Punycode approach. It essentially dooms non-American languages to second class status for a very long time. But it might be the expedient way to support IDNs. We'll see.