Abstract: A Eulerian two-fluid model based on the kinetic theory of granular flow is important for the calculation of large-scale multi-phase flows and reactions. The drag model which describes the interphase interactions is critical with respect to the calculation accuracy. This paper reviews various methods to develop drag models for dense heterogeneous gas-solid flows and discusses their merits and demerits. Based on the energy analysis of multi-phase flows, an energy minimization multi-scale (EMMS) drag model is established. The core of the EMMS model is the conservation equations of mechanical energy and the solution of such equations with the stability condition that the energy for the particle suspension and transport reaches the minimum. This paper discusses the development process of the EMMS model and points out its substantial defects in describing cluster characteristics. New descriptions of cluster characteristics are proposed and verified with experimental data. The predicted drag with the new cluster descriptions agrees well with experimental results, indicating the effectiveness of the model revision. Finally, this paper discusses the EMMS model defects in universal applications and suggests the developing directions.