The article tackles the issue of extradition in the aspect of its evolution and gives deep analysis of this notion at different stages of its development and in different epochs starting from the ancient times. The author enumerates several treaties on the issue and illustrates the development of the phenomenon of extradition on their basis. Apart from this, different aspects of extradition (such as refusal to extradite, consular courts, etc.) and their evolution are also analyzed. Theories concerning the issue of extradition are reviewed as well and their influence on the shaping of the concept in different countries and their respective legislations in this sphere is described. The author offers the analysis of the evolution of this concept in Russia thus demonstrating the importance of the concept of extradition in bilateral relations of the states. In the article the author has analyzed the evolution in history of the notion of extradition and thus has tried to convey its meaning. In this respect it is essential to remark that knowledge of the past events concerning the topic of the research may help understand further trends of the development of this phenomenon. This will also assist in assessing the influence it may have in the contemporary society.