This thesis looks at the dynamics between the concept of State sovereignty and the new international criminal law regime established by the Rome Statute. The principle of State sovereignty has served as a foundation of the international legal order for centuries because the State is traditionally considered to be the subject as well as the maker of international law. It is, however, a very contentious principle because many attempts have been made to give it a specific content, but this content has to be redefined in the light of modern trends and developments at the international level, which is then reflected at the national level. The concept has therefore always existed within an interstate paradigm, whereby States interact, cooperate and bargain with one another to serve and safeguard their own interests. However, the human rights movement has changed this state of affairs, and the creation of a permanent international criminal court represents a culmination of this movement. To understand whether and to what extent the content of State sovereignty is changing, the practice of criminal jurisdiction is assessed, both at the national level by the State and at the international level by the ICC. This assessment reveals two important issues. First of all, the international legal regime will be ineffective within the territorial boundaries of the State because, to some extent, State sovereignty remains somehow unchallenged in the context of international crimes, allowing States to retain the ability to grant amnesties or, in the context of State parties to the Rome Statute, to disregard the duty to ensure that perpetrators of international crimes do not go unpunished. Essentially, the balancing exercise concerning the codification of the Statute gives a greater deference to the State. In relation to the exercise of jurisdiction by the ICC, the paradigm changes from horizontal, governing the relationship between equal sovereign States, to a vertical one, centred on the relationship between State parties and the Court. This shift has given rise to some issues regarding cooperation, especially when the rules that apply within the horizontal system do not appear to be reciprocated within the vertical system. A better understanding of the true content of sovereignty can only be achieved through a clearer and more open evaluation concerning the place of State sovereignty in the intersection between the horizontal and vertical paradigms. A "renewed" understanding and content of sovereignty can lead to a more efficient surrender system in general. In addition, the lack of cooperation of member States in the arrest and surrender of President Al Bashir is indicative of the States' reluctance to violate another stronghold of international law, namely the immunity of a current Head of State. Without some international judicial collaboration between the relevant international courts, mainly the ICJ and the ICC, regarding a proper interpretation of immunity, cooperation concerning arrest and surrender will not reflect the general aim of the new regime, that is the end of a culture of impunity.