Emissions from aviation will continue to increase in the future, in contradiction of global climate policy objectives. Yet, airlines and airline organisations suggest that aviation will become climatically sustainable. This paper investigates this paradox by reviewing fuel-efficiency gains since the 1960s in comparison to aviation growth, and by linking these results to technology discourses, based on a two-tiered approach tracing technology-focused discourses over 20 years (1994-2013). Findings indicate that a wide range of solutions to growing emissions from aviation have been presented by industry, hyped in global media, and subsequently vanished to be replaced by new technology discourses. Redundant discourses often linger in the public domain, where they continue to be associated with industry aspirations of 'sustainable aviation' and 'zero-emission flight'. The paper highlights and discusses a number of technology discourses that constitute 'technology myths', and the role these 'myths' may be playing in the enduring but flawed promise of sustainable aviation. We conclude that technology myths require policy-makers to interpret and take into account technical uncertainty, which may result in inaction that continues to delay much needed progress in climate policy for aviation.