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This paper presents a review on various studies of flexible link manipulators which cover mathematical modeling and control of single link, two link and multi-link manipulators. This review has shown that the effectiveness of some controls such as Model Predictive Control (MPC) scheme alone and combined with Piezoelectric actuators (PZT), combination of robust nonlinear and fuzzy compensator, employing piezoelectric actuators by taking into account their position along the link, linear quadratic regulator (LQR), and fuzzy logic controllers. Based on the reviews, these control approaches are better than other control schemes to control the flexible link manipulators and vibrations suppression.