This book explores the Energy Minimization Multi-scale (EMMS) theory and the drag model for heterogeneous gas-solid fluidized flows. The results show that the cluster density plays a critical role with regard to drag. A novel cluster model is proposed and indicates that the profile of cluster density is single-peaked with the maximum value located at solid concentrations of 0.1~0.15. The EMMS theory is improved with the cluster model and an accurate drag model is developed. The model's universality is achieved by investigating the relationship between the heterogeneity and flow patterns. The drag model is subsequently verified numerically and experimentally.