The article discusses legal aspects of the application of the Framework Decision on the European Arrest Warrant (EAW) in the Polish legal order. The Framework Decision was adopted by the EU as a third-pillar legislative measure (concerning police and judicial cooperation in criminal matters) which obligated Member States to implement its provisions into their domestic legal systems. Satisfying this legal obligation by Poland by way of introducing amendments to its national legislation gave rise to many legal doubts of both theoretical and practical nature (the latter concerned e.g. establishing the legal status of the Framework Decision, identifying its consequences for Poland's domestic law, as well as determining the character of arrest warrant issued under the Decision, particularly in contrast to extradition, as well as mutual relations between the notions of EAW and extradition, between extradition and surrender. For the decisions concerning EAW are within the jurisdiction of domestic courts, one should recognize that the assessment of application of the provisions of the Framework Decision depends on the judicial practice of the courts. However, in case of any doubts on their part as to validity of domestic law and conformity of domestic legislation implementing the Framework Decision with the Constitution, the Constitutional Tribunal is an appropriate body to decide. As concerns the Framework Decision, such a procedure was once applied under Article 193 of the Constitution of the Republic of Poland, when the Constitutional Tribunal examined the conformity with the Constitution of Polish domestic law in respect of the admissibility of surrender of a Polish citizen (or a person which have been granted asylum in Poland) to another EU Member State under the EAW. The legal problems raised by the Constitutional Tribunal in its judgment, as well as those presented in jurisprudence of ordinary national courts in Poland, are not alone. This is proved by the practice of judicial bodies of other EU Member States, including the jurisprudence of constitutional courts. Court judgments concerning this issue are of interest to our country because they allow us not only to compare doubts raised in this respect and to justify and resolve them, but also to exert influence in a broader, not only domestic or European, but also international, context. The existence of such opportunity is indicated by the principle of reciprocity applied as a basis for refusal to execute an EAW. However, this principle does not ensue directly from the Framework Decision and has been inferred by the judicial practice from international law as a condition justifying non-execution of an obligation in case of international agreements. A practical extension of the systemic context of the Framework Decision leads to the situation when effects of domestic courts in relation to EAW may not only go beyond that instrument itself, but their consequences may also have impact on the effectiveness of the functioning of the entire legal system of the EU.