We propose a conceptual framework to explain why some technologies are more difficult to govern than others in global environmental governance. We start from the observation that some technologies pose transboundary environmental risks, some provide capacities for managing such risks, and some do both. For “ambiguous” technologies, potential risks and risk management capacities are uncertain, unknown or even unknowable. Governance systems are indeterminate towards ambiguous technologies, as existing norms, rules, scripts and routines do not imply default solutions under institutional focal points. Indeterminateness can lead to institutional drift, with risks accordingly remaining unmitigated and risk management capacities remaining unexploited. We use the cases of solar geoengineering, gene drive systems and bioinformatics for illustrating this framework. As technological ambiguity may often be irresolvable, we conclude that it might force us to confront the limits to anticipatory global decision-making on matters of long-term environmental sustainability.