Airborne wind energy (AWE) systems use tethered flying devices to harvest higher-altitude winds to produce electricity. For the success of the technology, it is crucial to understand how people perceive and respond to it. If concerns about the technology are not taken seriously, it could delay or prevent implementation, resulting in increased costs for project developers and a lower contribution to renewable energy targets. This literature review assessed the current state of knowledge on the social acceptance of AWE. A systematic literature search led to the identification of 40 relevant publications that were reviewed. The literature expected that the safety, visibility, acoustic emissions, ecological impacts, and the siting of AWE systems impact to which extent the technology will be accepted. The reviewed literature viewed the social acceptance of AWE optimistically but lacked scientific evidence to back up its claims. It seemed to overlook the fact that the impact of AWE’s characteristics (e.g., visibility) on people’s responses will also depend on a range of situational and psychological factors (e.g., the planning process, the community’s trust in project developers). Therefore, empirical social science research is needed to increase the field’s understanding of the acceptance of AWE and thereby facilitate development and deployment.