This diploma paper is about European Arrest Warrant as a warrant of the competent judicial authorities of the Member State of the European Union. It is a procedure, by a Member State against a person who is a citizen of another Member State of the European Union. This paper compares the conditions for issuing an Interpol arrest warrant and the European Arrest Warrant, as the two instruments which are closely related but not synonymous. It describes the legal practice in the Republic of Croatia and analyzes the legislative framework related to the European Arrest Warrant. It represents a new system of extradition by the European arrest warrant, which is considered more efficient than solving extradition and assistance in criminal matters under the Act of Mutual Legal Assistance in Criminal Matters. This paper represent its advantages and disadvantages. The paper describes the case of "Lex Perkovic" which was of the utmost importance to the Republic of Croatia. In conclusion, it describes the importance of the European arrest warrant as one of the most important instruments of judicial cooperation between Member States. Influence on the reduction of crime in the Member States.