Universal jurisdiction has a relatively long history. There is evidence from the seventeenth century of recourse to this legal institution as a means of avoiding the existence of areas of impunity. State practice, however, is quite recent, emerging from the concepts of war crimes and crimes against humanity. Regardless of how they are classified or categorised, it is within this framework that terrorist acts need to be viewed. The issue of the exercise of universal jurisdiction for crimes classed as terrorism arises when they are qualified by taking into account certain specific acts, such as serious violations of IHL, illegal seizure of aircraft, hostage-taking, kidnapping, acts committed with bombs, etc. Most treaties therefore provide for application of the principle of aut dedere aut judicare as a corollary to universal jurisdiction. However, conventional law, general or specific, is not the only basis for the exercise of universal jurisdiction in the case of terrorism offences. The customary basis is also very important, as are the unilateral acts of states when they legislate or pass judgement taking this framework — conventional or not— into account. The purpose of this article is to analyse all such aspects.