Advancements in electronics and software have enabled the rapid development of unmanned aerial vehicles (UAVs) and UAV-assisted applications. Although the mobility of UAVs allows for flexible deployment of networks, it introduces challenges regarding throughput, delay, cost, and energy. Therefore, path planning is an important aspect of UAV communications. Bio-inspired algorithms rely on the inspiration and principles of the biological evolution of nature to achieve robust survival techniques. However, the issues have many nonlinear constraints, which pose a number of problems such as time restrictions and high dimensionality. Recent trends tend to employ bio-inspired optimization algorithms, which are a potential method for handling difficult optimization problems, to address the issues associated with standard optimization algorithms. Focusing on these points, we investigate various bio-inspired algorithms for UAV path planning over the past decade. To the best of our knowledge, no survey on existing bio-inspired algorithms for UAV path planning has been reported in the literature. In this study, we investigate the prevailing bio-inspired algorithms extensively from the perspective of key features, working principles, advantages, and limitations. Subsequently, path planning algorithms are compared with each other in terms of their major features, characteristics, and performance factors. Furthermore, the challenges and future research trends in UAV path planning are summarized and discussed.