This chapter explains the work by the UN International Law Commission on the topic ‘Obligation to extradite or prosecute (aut dedere aut judicare)’ from 2006 to 2014, culminating in the Final Report of the Commission on this topic which was taken note of by the UN General Assembly in 2014. All the legal issues relevant to the obligation are identified and, where appropriate, analysed. The drafting history of the Report by the Working Group under the present author's chairmanship is elucidated in details — and this is the only place where this drafting history can be found.