The document analyzes the legislation of the Russian Federation and the member states of the European Union on extradition from the point of view of its compliance with the current European Convention on Extradition. It also makes proposals to improve the rules of the Criminal Procedure Code of the Russian Federation that regulates the extradition procedure. Methodologically, the work uses scientific methods of analysis and synthesis, as well as the historical, comparative method, all in an integrated approach. Among the conclusions, the fact that for the previous legal provisions to work, its consolidation only in the Code of Criminal Procedure of the Russian Federation is insufficient. The first step to put them into practice could be to discuss the issue of making the necessary amendments to the Convention on Legal Assistance and Legal Relations in Civil Matters, as well as in the Family and Criminal Affairs regulations of January 22, 1993, of which the countries of the European Convention on Extradition are parties.