The purpose of this article is to study the institute of the European Arrest Warrant, which appears as an immediate replacement of the extradition mechanism for the relations of capture and delivery of persons within the territory of the European Union. Based on the deductive methodology, we searched for doctrinal, legal and jurisprudential grounds to reach the present conclusions. Therefore, it’s necessary to analyze the context of emergence, your main operating guidelines and the principle of mutual recognition. Lastly, with the jurisprudential analysis of two relevant cases, it is sought to answer the basic: the possibility of the subject suffering cruel or degrading treatment in the prison system of the executing Member State can be treated as a hypothesis of not delivery?