The sustainability of air transport is increasingly studied in relation to climate issues. The objective of this paper is to provide the key elements for assessing whether a given transition scenario for aviation could be considered as sustainable in the context of the Paris Agreement. Addressing this question relies on a broad range of concepts which are reviewed. First, ethical considerations related to effort-sharing mitigation principles and physical considerations on climate impacts of aviation are introduced. Then, the technological levers of action for mitigating CO2 and non-CO2 effects are detailed. Concerning CO2 emissions, low-carbon alternative energy carriers represent the main lever, with a wide range of solutions with varying degrees of maturity and decarbonization potentials. Other significant CO2 levers include improving aircraft architecture efficiency and accelerating fleet renewal. Concerning non-CO2 effects, contrail effect mitigation through operational strategies is one of the most promising lever. Aviation transition scenarios are then reviewed, with a particular focus on scenario simulation and sustainability assessment methodologies. Prospective scenarios are a useful framework for assessing the impacts of technological levers on the achievement of climate objectives. This review leads to the conclusion that technological levers have an important role to play in making aviation sustainable; however, significant uncertainties weigh on their feasibility, particularly for the most ambitious scenarios which rely on strong technological and political trade-off assumptions. The paper ends by raising the question about the meaning of sustainable aviation, which must be based on technological but also, for instance, social, economic and ethical considerations.