Robots contribute significantly to different sectors of the economy, helping humans perform several tasks in different sectors. To do so, the robots must move from the initial position efficiently and smartly to their destination smoothly. The efficiency and intelligence with which robots move are critical for their effective functioning. Hence, new algorithms are required to help the robot move and perform the allocated task. Different algorithms are designed and available for the purpose, however, each has its benefits and drawbacks. This study reviews the different algorithms used in the movement of the robots to perform different functionalities. The classical, heuristic, and machine learning methods are analysed and summarised, highlighting each approach's advantages and disadvantages. By scrutinizing these algorithms, the study aims to provide a better understanding of the different attributes that reflect the performance of each of the algorithms. Moreover, suggestions for future research are presented, serving as a guide for researchers and scientists who are fascinated by robots and their movement. The study not only provides an understanding of the current algorithms but also provides direction for future advancements in the field.