When we talk about the challenges of the European and Albanian legislation on the surrender of persons wanted by criminal justice, the picture of the Albanian law and the operation of the law comes to mind. But today more and more measures are being taken to develop the legislative power and its functioning. These measures have also been taken in drafting and in administrative and judicial execution. Today, there is more and more talk about justice reforms; such are the challenges that Albania faces when it comes to cooperation with the EU in relation to the procedures for handing over persons wanted by law. It is such a challenge, because Albania’s legislation must be in line with that of the EU. When we talk about compliance or Acquis communautaire, we mean the interoperability that the legislative, judicial and executive powers must follow. Talking about the justice reform in Albania, we understand and analyse more closely the issue of corruption. The globalization of criminal activities has created a need to strengthen international cooperation. The investigation, prosecution and control of crime cannot be confined within national borders.