We sketch a novel mode of governance—'global ungovernance' (GU)—which draws on and informs the articles in this special issue. GU operates in the context of transnational institution-building projects which at once pursue big visions with claims to universality (eg, building 'markets' or the 'rule of law'), and at the same time offer no adequate prescriptions. We argue that the 'impossibility of closure' becomes a central problematic of practical activity in GU—by which we mean the ultimate practical impossibility of matching institutional structures with desired outcomes in these contexts. Viewed as a set of organised practices, GU evinces a commitment both to pursue closure and to embrace its impossibility, equally competently and even at the same time. As a result, GU changes the nature, purpose and conditions of possibility of institution-building techniques and practices.