Although many studies have been carried out on the way the law understands and deals with the digital revolution and particularly the Internet, we are unaware of any studies on the data sphere creating a new “space” for the law. This article, written as a result of discussions between a computer scientist and a lawyer, intends to challenge the constructions of international and European law as this new subject emerges and to examine relationships able to be formed with the territories. First, we need to define what the datasphere is and second, we will re-consider, by way of case study, four highly topical areas: A. Platform activity; B. The portability of digital content services in intellectual property law; C. The right to be delisted; and D. The transatlantic transfer of personal data.