The very long-awaited and anticipated top-level .EU domain has now been made available to the public for registration. As of today, registrars can begin taken requests, though the opening isn't completely finished. The release has been delayed for various reasons for a long time now, and during the initial “Sunrise” period of initial offering, only certain folk may apply:

”The launch of .eu will happen in several phases. The Sunrise period, during which only the holders of certain “prior rights” will be allowed to register their names, starts today at 11:00 CET”
A whois tool has already been in put into place and the eurid website contains a large amount of information concerning applications, registrar information and anything else you'd like to know about the new TLD.