The .eu TLD was passed by two recent European Regulations, in order to develop and improve the Information Society within the European Community and to make possible the visibility of the European Union, when undertakings and citizens use the .eu TLD in the digital networks. Moreover, the European Commission has chosen EURID in order to manage the .eu domain name. So this work, try to explain some important questions concerning to this issue in an easy way. Especially are explained different matters like the following: who is the Registry, who can act as registrar, who is entitled to apply for the .eu TLD, what kind of name can be registered, what happens if during the registration period the applicant dies or his company closes down and finally the Alternative Dispute Resolution procedure (ADR).