Continuously variable transmissions (CVT) have been widely used in many different areas such as automotive, robotics, manufacturing and aerospace industry. In CVT drives, a properly designed control strategy is needed to ensure the precise control of the speed ratio, and a deep knowledge of the steady-state and transient behavior of the drive is necessary to this purpose. In the framework of belt and chain CVT drives, model-based approaches developed for this purpose are mainly of two types: continuous models and multibody models. Continuous models are much less costly from a computation point of view, while multibody models are usually believed to be more accurate. The aim of this paper is twofold: first the CMM continuum model [Carbone G., Mangialardi L., Mantriota G., ASME Journal of Mechanical Design, 127, 103-113 (2005)] is compared with a multibody model of the chain-CVT variator. Secondly, the CMM model is proposed for a fast and enhanced characterization of the shifting dynamics of chain CVT. The analysis shows that, except for dynamical effects due to the intermittent contact of the chain pins with the pulleys and caused by the polygonal action of the chain, the CMM and multibody models provide very similar results. Moreover, this study shows, by exploiting the CMM model, that the overall dynamics of the CVT can be described by a relatively simple first order nonlinear differential equation, which can be very easily implemented for CVT real-time control applications. The accuracy of such a simplified approach is then tested against some preliminary shifting experiments under torque load conditions. Results show a very good agreement between theoretical predictions and experimental outcomes, thus making this simplified approach a promising tool to develop advanced real-time control of CVT transmissions for automotive applications. (C) 2016 Elsevier Ltd. All rights reserved.