Aviation is an important contributor to the global economy, satisfying society’s mobility needs. It contributes to climate change through CO₂ and non-CO₂ effects, including contrail-cirrus and ozone formation. There is currently significant interest in policies, regulations and research aiming to reduce aviation’s climate impact. Here we model the effect of these measures on global warming and perform a bottom-up analysis of potential technical improvements, challenging the assumptions of the targets for the sector with a number of scenarios up to 2100. We show that although the emissions targets for aviation are in line with the overall goals of the Paris Agreement, there is a high likelihood that the climate impact of aviation will not meet these goals. Our assessment includes feasible technological advancements and the availability of sustainable aviation fuels. This conclusion is robust for several COVID-19 recovery scenarios, including changes in travel behaviour.