<p>Optimal motion planning represents a crucial challenge in the areas of robotics and automation. As robots and automated machines are being engineered to function at increasingly higher speeds to achieve shorter production times, the demand for extreme performance from actuator controllers intensifies. However, operating at such high speeds can compromise the precision and repeatability of robotic movements. Creating a path is the main aim of path planning that takes the system from its initial position to a target destination, meeting critical criteria such as minimizing jerk, reducing trajectory completion time, optimizing energy usage, and avoiding obstacles, all while adhering to the dynamics of the manipulator's joints. This requires careful consideration to ensure that the trajectory can be executed at high speeds without causing excessive actuator accelerations or inducing vibrations in the mechanical structure. Given these challenges, trajectory planning algorithms are becoming increasingly essential in automation. This paper provides a systematic analysis and in-depth examination of various trajectory planning schemes used for selecting optimal paths for robotic manipulators, whether in Cartesian or Joint space. It also discusses optimal trajectory planning strategies that align with the manipulator kinematics and dynamics. A significant attention is placed on the application of genetic algorithms (GA) in motion planning to determine the most efficient trajectory path. Additionally, the paper explores hybrid optimization schemes that combine traditional algorithms with novel optimization techniques. The study analyzes and categorizes 211 research articles to provide an overview of the existing research on each trajectory planning schemes, with data presented through tables, charts, and figures showing the utilization of these algorithms concluded the past 20&#xa0;years. Based on the analysis, the paper identifies open research areas and challenges that remain in the field.</p>