This study presents a brief reference, in general, to international legal assistance in criminal matters, which is an extremely important field in international cooperation between states. In particular, we highlight certain approaches regard the most well-known form of judicial cooperation in criminal matters, without a doubt, namely extradition. The analysis included existing doctrinal concepts and legal provisions regarding the institution of extradition. They were taken into account several objectives, as: defining the concept of extradition; analysis of the legal nature of the extradition institution; elucidation of the forms, types and specifics of extradition in national legislation and at the same time, characterization of the institution of extradition as a form of international legal assistance in criminal matters. The used methods and procedures were determined by the emphasied interdisciplinary nature of the research subject. The investigation was based on the study of the normative and doctrinal material existing in the field, using diversified, various general and special methods in diachronic and synchronic plan. The novelty elements concern the scientific investigation of the extradition institution, of the specifics of its application. The investigation may be helpful both for academic environment and for practitioners, and will be included in a methodological-didactic material.