This article aims to present the results of a bibliometric analysis of relevant literature and discuss the main research streams related to the topic of risks in drone applications. The methodology of the conducted research consisted of five procedural steps, including the planning of the research, conducting a systematic review of the literature, proposing a classification framework corresponding to contemporary research trends related to the risk of drone applications, and compiling the characteristics of the publications assigned to each of the highlighted thematic groups. This systematic literature review used the PRISMA method. A total of 257 documents comprising articles and conference proceedings were analysed. On this basis, eight thematic categories related to the use of drones and the risks associated with their operation were distinguished. Due to the high content within two of these categories, a further division into subcategories was proposed to illustrate the research topics better. The conducted investigation made it possible to identify the current research trends related to the risk of drone use and pointed out the existing research gaps, both in the area of risk assessment methodology and in its application areas. The results obtained from the analysis can provide interesting material for both industry and academia.