Rotary Inverted Pendulum (RIP) is an under-actuated mechanical system which is inherently nonlinear and unstable. For decades, it has been widely used as an experimental setup to explain and test different kinds of control algorithms. The main control objectives of RIP are: Swing-up control, stabilization control, switching control and trajectory tracking control. All these control objectives are described in this study. State-of-the art works proposed for each control objective have also been reviewed. These comprise the linear, nonlinear time invariant, self-learning and adaptive nonlinear controllers. Moreover, different kinds of nonlinear dynamic models of the RIP together with the developed linear models in the literature have been analyzed. This is because most of the proposed controllers applied on RIP are found to be model dependent since they are mainly based on integral and/or invariant motion. Other types of RIP are also reported along with their advantages. Future research opportunities and challenges of the previous approaches in this area of research are presented. We believe that expert researchers can use this paper as starting point for further advancement while graduate scholars can use it as an initial point. (C) 2018 Elsevier Ltd. All rights reserved.