This book focuses on the modeling of gas-solid, liquid-solid, non-Newtonian fluid-solid, and supercritical fluid-solid fluidized beds and multiphase flows. Simulation techniques are categorized into Euler?Euler with kinetic theory of granular flow (KTGF) and Euler?Lagrange with discrete element method (DEM) approaches. Both the governing equations and numerical implementations are presented. A new CFD-KTGF-DEM approach describes phase interactions, free from the empirical restitution coefficient used in KTGF, and accounts for turbulence effects on discrete particle motion, which DEM cannot achieve. Additionally, a low Stokes number KTGF model is introduced, incorporating the interstitial fluid's effect, unlike the classical KTGF, which assumes vacuum conditions. Special attention is given to momentum exchange between heterogeneous and homogeneous flows in fluidized beds and multiphase systems, and various multiscale drag models are presented. The book also discusses the application of these approaches in fluid-solid fluidized bed reactors and oil-gas drilling processes.