The use of Unmanned Aerial Vehicles (UAVs), colloquially known as drones, has grown rapidly over the past two decades and continues to expand at a rapid pace. This has resulted in the production of many research papers addressing the use of UAVs in a variety of applications, such as forest firefighting. The main purpose of this paper is to provide a comprehensive overview of UAV-based forest-fire-extinguishing activity (FFEA) operations. To achieve this goal, a systematic literature review was conducted to answer a specific set of questions, which were carefully formulated to address the results of research conducted between 2008 and 2021. This study aims to (i) expand our understanding of the development of UAVs and their current contributions to the FFEA; (ii) identify particularly novel or unique applications and characteristics of UAV-based fire-extinguishing systems; (iii) provide guidance for exploring and revising further ideas in this field by identifying under-researched topics and other areas in which more contributions are needed; and (iv) explore the feasibility of using UAV swarms to enable autonomous firefighting in the forest without human intervention. Of the 1353 articles systematically searched across five databases (Google Scholar, ACM Digital Library, Science Direct, Scopus, and IEEE Explore), 51 highly relevant articles were found to meet the inclusion criteria; therefore, they were analyzed and discussed. The results identified several gaps in this field of study among them the complexity of coordination in multi-robotic systems, the lack of evaluation and implementation of fire extinguishing systems, the inability of handling multiple spot fires, and poor management of time and resources. Finally, based on the conducted review, this paper provides significant research directions that require further investigations by researchers in this field including, the deployment of UAV-based Swarm Robotics, further study on the characteristics of the fire extinguishing systems; design more effective area coverage; and the propose of a self-firefighting model that enables individuals to decide on the course of events efficiently and locally for better utilization and management of time and resources.