This paper presents an overview of the physical models for computational fluid dynamic (CFD) predictions of multiphase flows. The governing equations and closure models are derived and presented for fluid-solid flows and fluid-fluid flows, both in an Eulerian and a Lagrangian framework. Some results obtained with these equations are presented. Finally, the capabilities and limitations of multiphase CFD are discussed. (C) 2003 Elsevier B.V. All rights reserved.