Sustainable aviation practices have significantly reduced the Greenhouse Gas (GHG) emissions over the years. However, these practices have not shaped the aviation industry in achieving the United Nations Sustainable Development Goals (UN SDGs) to its full potential. The increasing volume of air traffic and the benefits reaped in this sector has hindered sustainable airline operations. This paper brings up a small scale-literature review on several tools and methods used for sustainability assessment in the aviation industry to address this concern, covering all the socio-economic and environmental dimensions of sustainability. A review on various models and techniques used in the eco-efficiency assessment for sustainable airline operations are also discussed. Decision Support Systems (DSS) using Artificial Intelligence (AI), Deep learning and Neural Network (NN) models also formed the basis of this study. These tools and models discussed in this paper support both the strategic and tactical decision making in order to foster sustainable operations in the aviation industry thus, helping mitigate the current challenges.