Starting from the first Greek judicial decision relative to domain names, the author presents the issue of protecting distinctive signs in case they are used by third parties as an Internet address. In the first section he makes a brief introduction into the technical and organisational peculiarities of the domain names and in the following sections he examines the legal problems from the aspects of trademark law, unfair competition law, law of tort and protection of the name. By providing examples from other countries' case law, where similar cases have arisen, he displays the potential as well as the limits of the traditional law of distinctive signs in the digital world.