The application of drones to assist with healthcare delivery has grown rapidly over the last decade. This industry is supported by a growing research field, and we have undertaken a systematic review of the published literature. Web-based searches returned 290 relevant manuscripts published between 2010 and 2024. We applied Topic Modelling to this corpus of literature, which examines word association and connectedness within the research papers. The modelling identified two emerging research themes with little connection between them: those who used drones to deliver time-critical medical items and those who used drones to deliver non-time-critical medical items. The former was in response to medical emergencies, while the latter was for enhancing resilience in the healthcare supply chain. The topics within these research themes exhibited notable differences. The delivery of time-critical medical items theme comprised the topics of ‘Emergency Response’, ‘Defibrillator and Organ Delivery’, and ‘Search and Rescue’, whilst non-time-critical delivery researched the topics of ‘Supply Chain Optimisation’ and ‘Cost-Effectiveness’, ‘Overcoming Remoteness’, and ‘Pandemic Response’. Research on ‘Engineering and Design Considerations’ and ‘Ethical and Social Considerations’ cut across both research themes. We undertook further analysis to assess research topic alignment and identify knowledge gaps. We found that efforts are needed to establish a more standardised terminology for better alignment across the two emerging research themes. Future studies should focus on evaluating the impact of drone delivery on patient health using systematic methods. Additionally, exploring the economic viability of drone-based health services and addressing regulatory barriers are crucial for efficient and effective drone deployment in healthcare delivery systems.