Full text can be accessed at http://link.springer.com/chapter/10.1007/978-94-6265-041-1_4A state wishing to punish the core crimes under international law in its domestic courts can choose to follow two approaches. The first is to prosecute those crimes by relying on its ordinary domestic criminal law. The second approach is to prosecute them by relying on the structure of international criminal law as it is or as modified. The effectiveness of the first approach depends largely on how broadly or narrowly the domestic criminal law is structured, whereas that of the second approach depends, inter alia, on the practice followed in that state as regards domestication of international law norms so as to make them enforceable in the domestic courts. This chapter examines the two approaches in relation to the crimes against humanity allegedly committed in Kenya during the post-election violence, and evaluates whether Kenya has or could have utilized any of the approaches to effectively prosecute and punish the main perpetrators of these crimes. This discussion will provide a model for other jurisdictions, especially in the developing countries, that wish to address impunity for the core crimes in their domestic courts.