The widespread interest in using drones in maritime transport has rapidly grown alongside the development of unmanned ships and drones. To stimulate growth and address the associated technical challenges, this paper systematically reviews the relevant research progress, classification, applications, technical challenges, and possible solutions related to the use of drones in the maritime sector. The findings provide an overview of the state of the art of the applications of drones in the maritime industry over the past 20 years and identify the existing problems and bottlenecks in this field. A new classification scheme is established based on their flight characteristics to aid in distinguishing drones’ applications in maritime transport. Further, this paper discusses the specific use cases and technical aspects of drones in maritime rescue, safety, navigation, environment, communication, and other aspects, providing in-depth guidance on the future development of different mainstream applications. Lastly, the challenges facing drones in these applications are identified, and the corresponding solutions are proposed to address them. This research offers pivotal insights and pertinent knowledge beneficial to various entities such as maritime regulatory bodies, shipping firms, academic institutions, and enterprises engaged in drone production. This paper makes new contributions in terms of the comprehensive analysis and discussion of the application of drones in maritime transport and the provision of guidance and support for promoting their further development and integration with intelligent transport.