Flying Ad hoc Network (FANET) is a self-organizing wireless network that constitutes swarms of flying nodes, namely Unmanned Aerial Vehicles (UAV), and communicates in close proximity. It has various distinguishing characteristics that set it apart from other ad hoc networks, posing some issues, particularly in routing. UAVs are highly dynamic and have frequent topology changes. Hence, the network urges an efficient routing technique to coordinate the node swarms and enhance the evaluation metrics of the network. The biological behavior of various living organisms, such as animals, insects, microbes, and humans, inspires researchers to solve various routing problems in ad hoc networks. Decentralized self-organized swarms of UAVs closely resemble the biological system. Therefore, the Bio-Inspired Algorithms (BIA) resolve a wide range of routing challenges in FANET. A Systematic Literature Review (SLR) is adopted to survey FANET routing methods based on non-hybrid and hybrid BIAs to properly comprehend the existing bio-inspired strategies used in FANET routing. The review will be beneficial for the researchers in the specified area. To our knowledge, no SLR has been conducted about the FANET routing protocol that employs BIA. This paper examines (1) the characteristics and features of existing routing algorithms, (2) the need of both non-hybrid and hybrid BIA for effective and optimal routing, (3) an analysis of the method's simulation tools, evaluation metrics, and mobility models, (4) the current issues and scope of the study related to the specified method.INDEX TERMS Bio-Inspired Algorithm (BIA), Flying Ad hoc Networks (FANET), Metaheuristic optimization, Systematic Literature Review (SLR), Unmanned Aerial Vehicle (UAV).