In recent decades, flexible manipulators have been studied by many researchers from robotics, solid mechanics, and control fields. Flexible manipulators have many advantages, including low weight because of the slenderness of the links of the robot. Although the original objective was to take advantages of the slenderness or flexibility in real robots, the challenging dynamics of the systems intrigued interests to employ an experimental flexible manipulator as a test bed to evaluate different modelling or control methods. With such a vast and various literatures, a review is indispensable for researchers who want to adapt their interests with the area. Some valuable review articles have been published, referencing numerous articles on single-link or multi-link flexible arms. This article pays an inclusive focus on trends of the research on modelling and control of multi-link flexible-link manipulators. The scope of this review article is particularly on two-link flexible manipulators, relevant models presented for closed-loop applications, and model-based control. Recent and historical contributions in the modelling and control of flexible-link manipulators are presented and discussed. As regular industrial manipulators normally have multiple links with two long links, that is, upper arm and forearm, this review can introduce advances in considering elasticity effects to robotic researchers.