Robot manipulators are widely used in many fields and play a vital role in the assembly, maintenance, and servicing of future complex in-orbit infrastructures. They are also helpful in areas where it is undesirable for humans to go, for instance, during undersea exploration, in radioactive surroundings, and other hazardous places. Robotic manipulators are highly coupled and non-linear multivariable mechanical systems designed to perform one of these specific tasks. Further, the time-varying constraints and uncertainties of robotic manipulators will adversely affect the characteristics and response of these systems. Therefore, these systems require effective modelling and robust controllers to handle such complexities, which is challenging for control engineers. To solve this problem, many researchers have used the fractional-order concept in the modelling and control of robotic manipulators; yet it remains a challenge. This review paper presents comprehensive and significant research on state-of-the-art fractional-order modelling and control strategies for robotic manipulators. It also aims to provide a control engineering community for better understanding and up-to-date knowledge of fractional-order modelling, control trends, and future directions. The main table summarises around 95 works closely related to the mentioned issue. Key areas focused on include modelling, fractional-order modelling type, model order, fractional-order control, controller parameters, comparison controllers, tuning techniques, objective function, fractional-order definitions and approximation techniques, simulation tools and validation type. Trends for existing research have been broadly studied and depicted graphically. Further, future perspective and research gaps have also been discussed comprehensively. © 2023 by the authors.