A system that can fly off and touches down to execute particular tasks is a flying robot. Nowadays, these flying robots are capable of flying without human control and make decisions according to the situation with the help of onboard sensors and controllers. Among flying robots, Unmanned Aerial Vehicles (UAVs) are highly attractive and applicable for military and civilian purposes. These applications require motion planning of UAVs along with collision avoidance protocols to get better robustness and a faster convergence rate to meet the target. Further, the optimization algorithm improves the performance of the system and minimizes the convergence error. In this survey, diverse scholarly articles were gathered to highlight the motion planning for UAVs that use bio-inspired algorithms. This study will assist researchers in understanding the latest work done in the motion planning of UAVs through various optimization techniques. Moreover, this review presents the contributions and limitations of every article to show the effectiveness of the proposed work.