Aviation accounts for approximately five percent of global greenhouse gas emissions through the combustion of fossil fuels. This paper analyses the opportunities and challenges of mitigation measures in limiting travel volume, energy and emission intensity to reduce the climate impact of aviation in Sweden. Several measures are in place that aim to reduce the climate impact of the aviation industry, ranging from regulations to technology alternatives to fossil-based jet fuel. These measures face several crosscutting challenges, many of which are of a socio-economic and political nature, and these aspects are often neglected in favour of focusing on technological solutions. The market creation for alternatives to fossil-based jet fuel is a major challenge, as most consumers today have a limited awareness of and willingness to pay for these innovations. Policy measures in place are proven ineffective in incentivising change. An understanding of the industry as a socio-technical system is required. The value of this review is its broader consideration of the pathways to reduce aviation's climate impact, offering new perspectives and pointing to areas for further research considering all components, their interactions and interdependence.