The environmental impacts of the international aviation industry are increasingly becoming the focus of public debate, forcing both airlines and aircraft manufacturers to integrate sustainability into their future decision-making processes. As a method for quantifying environmental impacts, Life Cycle Assessment (LCA) is able to support decision-making processes for the operationalization of sustainability goals. Life cycle assessments are already being used by researchers and practitioners in the aviation industry. This paper examines the current status of LCA applications, methodological approaches and challenges in aviation by means of a systematic literature review and focuses on contributions that are outside the scope of sustainable aviation fuel. After screening 1117 contributions, 45 contributions were considered in the analysis of the methodological implementation. Based on this analysis, challenges and further research requirements were identified. The paper concludes by proposing a framework for conducting LCA in the aviation industry.