The contradiction between the rapid development of aviation market and supply of airspace resources has increased the environmental damages of aviation carbon emission. The conversion and application of environmental damage assessment method of aviation carbon emission were summarized, and the characteristics of the assessment methods for air and ground transportation were compared. We found out the followings: \mathrm{①} The evaluation method has been transformed from static assessment to dynamic evaluation, and focused on four key problems, average and total carbon emissions, airspace resource utilization, LTO stage emission, and reduction practice; \mathrm{②} Airport terminal area as well as LTO are becoming the focus in the study of aviation carbon emission assessment method, while the former is the main area and the latter is the main stage of aviation carbon emission. The practice of emission reduction is mainly reflected in the optimization of emission reduction measures in economic field; \mathrm{③} Based on the situation and total assessment methods, environmental damage assessment and comparative advantage of aviation carbon emission and ground transportation carbon emission are reflected in the distance by using distance factor and energy consumption; \mathrm{④} Improving the smoothness of airspace resource traffic network, optimizing flight schedule structure and airspace resource allocation are more conducive to promoting aviation emission reduction.