Communication via air routes is an important issue in a world organized around a web city network. In this context, the robustness of network infrastructures, e.g. air transport networks, are a central issue in transport geography. Disruption of communication links by intentional causes (e.g., terrorist attack on an airport) or unintentional (e.g., weather inclemency) could be crucial for countries, regions and even the airlines affected themselves. Policymakers and the management of airlines and alliances should be able to reduce the effects of such interruptions in order to ensure good communication through air transport (i.e., maximize the robustness of their network at a reasonable cost). The literature review of the study of air transport route networks through an analysis of complex networks has highlighted a lack of contributions to the study of the topology and the robustness of such networks which contrasts, with advances undertaken for other transport networks or communication systems. This survey suggests areas in which research should be undertaken, based on the existing literature in other areas and from three different perspectives: global route networks, airline alliances, airlines and airports so as to help towards a better understanding of air traffic and, therefore, to be able to assess the potential damage of any airport being inoperative for a continent, country or airline.