This chapter concerns an issue of vital importance for every international criminal tribunal, obviously including the International Criminal Court (ICC). The author notices that without its own police force, the ICC relies on cooperation from states to perform its mandate which is—nevertheless—not always forthcoming. In many circumstances, the ICC requires cooperation from states that are not parties to the Rome Statute that created it. Obtaining cooperation from these non-state parties is complicated by the fact that they do not have the relatively clear and binding cooperation obligations under that treaty that state parties have. One underexplored aspect of this much-discussed quandary is the potential for non-state parties to have cooperation obligations under other international human rights and humanitarian law treaties to which they are parties. Given the key role that the ICC plays in the enforcement of international humanitarian law and particularly the Geneva Conventions, this chapter explores this potential by investigating possible obligations to cooperate with these tribunals under all four Geneva Conventions and their Additional Protocols. It examines potential cooperation obligations under both the specific prosecution obligation in the grave breaches provisions and the more general Common Article 1 obligation to ensure respect for the conventions. The chapter also highlights the role that such an obligation could play in current geopolitical crises, such as the Russian invasion of Ukraine.