Hegemony suffers from a bad press. It is currently used to refer simply to United States primacy. Thus presented, the US is considered to have been hegemonic since 1945, or at least since 1990. Instead, hegemony is presented here as a legitimate institution of international society in which special rights and responsibilities are conferred on the hegemon. No such hegemony exists at present. However, given today's constellation of power, a circumscribed US hegemony potentially has a distinctive contribution to make to contemporary international order. To map out such a hegemonic institution, this article reviews some historical precedents. It finds that, rather than uniform, these have taken a variety of forms, especially with respect to the scope of the legitimacy and constituency within which they have operated. A scheme of hegemonies—singular, collective and coalitional—is set out as a more realistic way of thinking about hegemony's present potential.