Atrocious crimes have been committed in the course of several wars that plagued the course of history. Consequently, a crusade over several centuries culminated in a treaty – the Rome Statute which for the first time in human history, created the ICC, an independent and permanent Court to investigate and prosecute heinous crimes committed in the course of wars and violent conflicts but in certain specific circumstances. Crucially, the Rome Statute explicitly repudiates all forms of exemption from criminal responsibility. A cornerstone for the operation of the Court is the principles of complimentary which reiterates the primacy of national judicial processes. Only when a state is either unwilling or unable genuinely to investigate and prosecute a case may the Court's jurisdiction be activated. A decade after the Court became operational, it has faced pressure and accusations of among others, whittling away state sovereignty and undertaking selective prosecution especially targeting Africans. In light of these serious allegations from erstwhile supports turned critics of the Court, the study, using largely the grounded theory methodology premised on a qualitative research paradigm, examined the veracity of and sough the theoretical foundations of these accusations. In addition, the study critically discussed the twin notion of unwillingness and inability which underpins the principle of complementarity. One of the findings of the study was that despite strong claims from political elites from political elites from some state parties, the assertion that the Court severely undermines state sovereignty and targeting the African continent is untenable. Accordingly, a theory of self-interest emerged as a plausible explanation for criticisms levelled against the Court. A critical examination of the Court's application of the unwillingness and inability test showed contrary to the initial fear that absence of a precise definitions would be hamper the jurisdiction of the Court, it on the contrary permit progressive flexibility. A conclusion from the study was that, although not etched as a universally accepted customary law, sovereignty and immunity cannot be an excuse for culpability for commission of crimes that causes outrage against humanity. Despite challenges that it faces, the ICC offers the best prospect of being an effective deterrence and accountability for unimaginable atrocities that hitherto have deeply shocked humanity's conscience and threatened world peace and security. It is for this reasons the study reiterated calls for unflinching support for the Court and its protection from political pressures and interferences in performance of its noble mandate.